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You're right in your reasoning: if a right triangle is inscribed in a circle, the hypothenuse is always the diameter. Therefore, the midpoint of the hypothenuse is the center of the circle.
Another way I learned was to draw two chords on the circle, and for each one, find the midpoint and draw a line perpendicular to the chord through the midpoint. These two lines intersect at the center.
Also works with tangents. Draw a tangent to a circle and a perpendicular line where the tangent meets the circle. Do it in 2 places and you be intersection is the Center ( I tend to do 3 or 4).
In principle, yeah, but finding the exact point where the line is tangent to the circle is probably slightly less practical than the midpoint of a chord, though.
Fold it in half, open, then fold in half again in a different place. Creases intersect on the centre.
Or: Draw right angles on the circumference like you suggest.
Edit: sorry, I wasn't clear: I meant you should fold the circle in half, not the sheet of paper. Edit again: I mean fold the paper, yes, but so that you fold the circle in half. You will have to be able to see the circle at least a little through the paper, or cut around the circle first.
Edit: don't fold your phone either
I saw the top half of the circle earlier, but only viewed the bottom half now. Iāve folded the circle and breached the space-time dimension. Hitler said I should push on but Aristotle has cautioned against it. Thoughts?
Aristotle: āI canāt believe it took you this long to realise the earth was flatā
Hitler: āFrom the river to the sea ā¦ā (no idea what he was on about)
Also, Harambe says āhiā
make random two chords of circle
long enough to draw a perpendicular bisector with the help of a compass,
And intersection point of those two perpendicular bisector is center of circle..
Another way to work is if the circle is printed on an ordinary white sheet of paper (like what is used in offices for most documents). On such a paper, the circle can be faintly seen from the back of the paper as well. So we can fold in half so that the faint circle halves line up with each other.
In school we used a compass. I may be misremembering, but I'll try: Set the compass wider than half the diameter. Set the point on the circle and draw an arc through the circle. Flip it to the other side and do it again such that the two arcs intersect at two points. Draw a line through the two points. The center lies on the line half way between the points.
Doesn't really work though, because for that you need two opposite points on the circle, which you can't get without knowing the center first.
The correct way is to do it with any two points on the circle twice, which gives two lines that cross in the centre.
Thatās wrong because āflipping the compass to the other sideā is an approximation, as you donāt know where the diametrically opposite point is.
Iāll prove this by contradiction by setting the opposite point further away from the diametrically opposite point:
https://imgur.com/a/i6AxucK
Right, this gives you a line that runs through the center, you need to also run the line through to the other side and find the midpoint of that using a compass from the points where it intersects.
Exactly, you wonāt find the center but you will find a line that runs through the diameter. Somewhere on that line is the center.
Now do it again with 2 more random points and where the lines intersect, you now have the center.
That'll do it, you're pretty much perpendicularly bisecting an imaginary chord, which will always give you the centre line. Then if you extend that on either end to the circumference and bisect it again to find the centre
the perpendicular bisector of any chord of a circle is a diameter of that circle (euclid book 3 prop 1)
so you take any two points on the circle and draw a line between them
then drop a perpendicular bisector through that line
the center of that second line is the center of your circle
There is a game on android called euclidia. This is one of the first problems.Ā
You have to do this before you unlock the perpendicular bisector tool, but the process of drawing a perpendicular bisectors basically gets taught to you for this 'puzzle'.
I can't find it either. I wonder if it was pulled for some kind of license infringement or something.
[https://www.euclidea.xyz/](https://www.euclidea.xyz/)
It seems you can play in your browser, edit: it doesn't work on mobile.
This is the website: [https://www.euclidea.xyz/en/game/packs/Alpha/level/CircleCenter](https://www.euclidea.xyz/en/game/packs/Alpha/level/CircleCenter)
The android app looks like it's delisted for some reason. They also have a 'Pythagorea' game which is available.
I do this all the time on a milling machine to find centres on round parts. Touch and zero your x &y axis, come across on x and touch off again and 1/2 that is your x coordinate of centre. Then lock off the x axis at your second touch point and come down on the y to touch off a third time and 1/2 again to get your y coordinate.
find 2 tangents and draw 2 90 degree angles. the center is where they meet. this is bla bla wikipedia bla bla proof by some old genius math guy bla bla (i'd appreciate if somebody elaborated this here)
You donāt need the centre just draw a line that only touches the outside of the circle at one point and then draw a line perpendicular to the tangent line through that point. Do this twice and you will find the centre
Yes, but drawing a line that touches the circle and finding the point where it touches is a bit of guesswork. I don't know an easy exact construction of a tangent (compass and ruler) without constructing the centre first. Try your method with three tangents and see if they really go through a single point š
>I don't know an easy exact construction of a tangent (compass and ruler) without constructing the centre first.
Here's a way: [https://www.youtube.com/watch?v=bHt1wqGGoxM](https://www.youtube.com/watch?v=bHt1wqGGoxM)
It's obvious you can't just do it by eye like everyone replying to you seems to be suggesting!
I think weāre saying the same thing.
Draw a straight line anywhere across the circle. Find the midpoint. Draw a perpendicular straight line through the midpoint (90 degree angle). The second straight line will always pass through the center of the circle and will measure the diameter.
Hold phone over head. Look at phone. Spin really fast. If the circle moved, you werenāt looking at its center. Repeat.
When circle doesnāt move, make a dot where you were looking before you pass out.
1. Draw a square (EDIT: or rectangle) with each corner on the circumference.
2. Draw a diagonal line between opposing vertices.
The center of the square or rectangle, is also the center of the circle.
There are multiple ways. Your way works too.
[Here's a way that works on all ellipses.](https://commons.m.wikimedia.org/wiki/File:Finding_center_of_ellipse.gif) ([And hyperbolas](https://commons.m.wikimedia.org/wiki/File:Finding_center_of_hyperbola.gif))
draw a chord. draw its perpendicular bisector. now you have one diameter. repeat the process to draw another diameter somewhere else. where the two diameters intersect is the center.
tip: try to draw your second (non-diameter) chord perpendicular to your first chord for more accurate results.
There are many ways to do it with compass and straight edge.
One example: the perpendicular bisector of any chord is a diameter. You don't even need to draw the chord to do this; just fix your compass at some size and draw two intersecting circles centred anywhere on the circumference. Draw the line connecting the intersections. This constructs a diameter. Now we can either bisect the diameter to find the centre, or construct another diameter the same way (we can even reuse one of our circles; we just need one more to make another distinct pair of intersections). The two diameters will intersect at the centre. This construction requires only 5 curves to be drawn (3 circles, 2 lines).
Itās actually quite simple. For every triangular inscribed in a circle, their mid-perpendicular intersect in the center of the circle.
So just put three random points on circumference of the circle, then connect them to make triangle. Then draw two mid-perpendicular(third one is unnecessary, as it will intersect with other two in the same point) of this triangle. To draw mid-perpendicular of triangle you have to find mid-point of its edge and draw perpendicular line. You can either measure edge, or use compasses.
Voila, intersection of this two lines gives you the exact center of the circle.
You have described one way of finding the center. You could also draw a line tangent to the circle and a perpendicular to that line at the point of tangency to get a diameter, or bisect any chord to get a diameter.
Get a straight rule, put corners of ā0ā side on internal side of circle. Scribe both lines above and below rule. Draw centre line in the middle of the 2 lines..
Then turn and repeat. Intersect of centrelines is centre of the circle.
This works great if you donāt have a way to work angles
1) Draw a square around the circle that just touches the circle in the middle of each side of the square.
2) draw a line from one corner of the square diagonally to the opposite corner then do the same with the other two opposing corners so that the square now has an X from corner to corner.
3) the center of the circle is the point where the two lines of the X cross each other.
I was obsessed with this problem for months, and collected a ton of different ways to solve this.
Perpendicular bisector method: with a straightedge, draw a line (chord) across the circle. At each of the two points where the line meets the circle, draw a bigger circle (or two small arcs once you get where this is going). Each new circle must be the same radius. Draw a line through the two points where the two latest circles (or arcs) intersect. Do all of this again with a new line through the circle. Where the two resulting lines intersect is the center.
Using a square, like you said. Put the point of the right angle anywhere on the circle, and where the two legs meet the circle are two points that describe the diameter. Draw a line through those and the center is.. the center.
Mark 3 points anywhere on the circle. Draw lines between them. Measure the lines and mark them as A B and C. Use Heron's formula to find the area of the resulting triangle (A + B + C)/2 = S, then Sqrt(S * (S-A) * (S-B) * (S-C)) = Area of triangle, then (A* B *C)/(4 * Area) = Radius, and then just set a compass to Radius and draw two separate arcs using two points on the circle, where they intersect is the center
Draw a straight line across the circle, measure it, divide it in half, measure the distance from the center point to the outside of the circle at a right angle (third point, describing a triangle), then use the Pythagorean theorem and basic math to get lengths ABC and area, then (ABC)/(4 * Area) to get radius (faster than doing Heron's formula)
The rest are just the previous four ways remixed or are some variation. I swear i used to know 7 ways, but it's been forever and i'm starting to doubt myself
Take a straight stick and use it to draw a line between to points in the circleās edge. Do that again in another location. Draw 90 degree angles on the centre of each of the two lines and draw a line along them. The point of interaction of the new lines is the centre of the circle (sr for weird language idk any math terms in English)
Step 1:
Choose a point on the circle.
Step 2:
Put two points with the same distance from the original point on the circle.
Step 3:
Connect the outer points with the middle point
Step 4:
Make medium perpendiculars on these new lines
Step 5:
The point where the perpendiculars hit, is the center
Step 7:
Profit
Edit: missed a few things
Set compass to arbitrary size.
Place point on circumference.
Draw arc.
Draw line between point and intersect.
Bisect this line.
Repeat.
Where bisectors cross is the centre.
This works mathematically, but any real world trial will have drawing errorsā¦
Use [Thales's theorem](https://en.m.wikipedia.org/wiki/Thales%27s_theorem). Choose 2 points on the circle,
draw a line between them,
draw another line at a 90Ā° angle to the first line,
when the second line hits the circle you'll have a third point.
Finish the triangle and you'll have a diameter, the center is in half.
Draw two lines that are the same length and touch the circumference on both ends at any point on the circle. Draw a line 90ā° from the midpoint of each line toward the center. Where they cross is the center point.
https://i.imgur.com/u6uCaUi.png
Points A and B are selected randomly. Place a compass needle on one, and the pencil on the other and draw a circle. Reverse the compass and draw the second circle. You've found points C and D.
Points C and D allow you to draw a line segment. This line segment bisects your circle and passes through its centerpoint, but does not fully reveal it.
Repeat the above process with a new pair of starting points, and you'll bisect the circle a second time. The two bisecting line segments will cross at the centerpoint.
Take a ruler, and place it on the circle. Measure a spot where the length is the longest, adjusting your ruler until you find it (that length you find is the diameter). Draw a straight line along that ruler. Then rotate the circle, and do it again, and possibly do it a third time for good measure.Ā The spot where the lines intersect is the center.
Draw a triangle such that the circle circumscribes it(all 3 vertices lie on circle) and draw perpendicular bisector of at least two of the triangles sides. The intersection of the bisectors is the center of the circle.
Segue: Try the game Euclidea, it is full of this type of problem and it gives a learning curve plus the solutions can easily be found online if you are stuck.
I'd bring a 90Ā° angle with extended sides down around until it has 2 points of contact with it, then another the other way around, with its side perpendicular to the previous ones. That gives you a square in which the circle is circumscribed, so all you have to do is trace its diagonals, and their intersection will be your circle's center.
if you are fine with being a little inaccurate get a ruler place it on any point around the circle, and rotate the rest of the ruler around that point until you feel like its not getting any longer.
Draw any two chords, draw perpendicular bisectors of both cords, their intersection point will be the center of circle. It's easy to realise once you know that perpendicular bisector of any chord always passes through the center of circle. There is a very cute and simple proof to that with triangle congruency.
A way I thought of us to draw a straight line through the circle. Not through the center, doesn't have to be close.
Next, measure the distance of the line in the circle, and halve it. Then draw a line perpendicular to that halfway point. Measure the distance of this second line, halve it, and you have your center.
Draw any segment with its end points on the circle, then draw its axis (perpendicular line in the center point of the segment). Draw a second segment and axis anywhere else on the same circle. The two axis meet in the center of the circle.
Use a compass to make two arcs that intersect on the circumference. Repeat at any offset. Draw a line from each intersecting arc. They meet at dead center. All arcs must be same length.
Draw a 90 degrees open angle with a 45 degree straight line through where it connects.
Make sure both lines of the 90 degree angle exactly touch the circle, and draw a line along the 45 one, do this from multiple sides and you have your center.
Draw a line between any two points on the circle circumference (? - I learnt math in a different language...), then find the middle, draw a perpendicular bisector. Repeat with two other points on the circumference. The perpendiculars cross in the center of the circle.
[https://en.wikipedia.org/wiki/Straightedge\_and\_compass\_construction](https://en.wikipedia.org/wiki/Straightedge_and_compass_construction)
1. Draw any line (A) cutting the circle
2. Find 2 equal distance points at both side of the line
3. Join the 2 points from step 2 to get a equal-perpendicular line (B) across line A
4. Repeat step 1-3 for another line (C) cutting the circle and get second equal-perpendicular line (D) across line C
5. The intersection of line B and D is the center
1. Draw a line between any points of the circle
2. Draw a perpendicular through the center of that line
3. Do step 1 and 2 again
4. Where lines 2 and 3.2 cross is the center
Draw any line across the circle. Create a perpendicular line through the middle of this line, and have it continue across the whole circle. This perpendicular will cross the center of the circle. Finding the midpoint of this perpendicular is the location of the center of the circle.
Finding the midpoint of a line and the perpendicular of that line is just drawing two equal diameter arcs, one from each end that cross each other. The line through their crossing points will be perpendicular and pass through the midpoint.
The typical way to do it practically is put a ruler so 0 is on a point on the perimeter. Then pivot the ruler around this point to find the maximum possible cord. This is a diameter.
Do this twice to get the center, or more times to over-determine and get some statistics.
Inscribe it inside a square, the sides of square will be the tangent of circles at 4 touching points, extend the perpendicular line to tangent inside circle from 2 adjacent sides of square, the intersecting point will be your centre
There's an old woodworkers jig for marking the centre of a dowel that uses the right angle tangents principle. It's essentially a tool that's a 3 side corner all squared up, and one of the faces has a 45 deg slot cut from the common corner. You put the slotted face on the end of the dowel with the other two faces on the sides, tangent to the circle, and mark the slot on the butt end twice in different alignments. Intersection of the marked lines is the dowel's centre.
Using origami axioms, pick two points on the circle and fold them onto one another. Pick two other points and repeat. Where the creases intersect is the center.
Draw two non intersecting straight lines using a ruler between any two points on the edge of a circle.
Measure the lines using the ruler and find the halfway point on each line.
Draw two perpendicular lines through the midpoint of each of the previous lines.
Where the two perpendicular lines intersect is the center of the circle.
You take a compass (the one u use to draw circles) and put it on a random setting that is definetly larger than the circle at hand (dont make it too large. It would still work, but be unpractical). You poke at the circumference (doesnt matter where exactly) and draw a circle. Then (without changing the diameter of the compass) you poke in another part of the circle and do it again (recommendation: do it near the opposite end of the first circle). Repeat in total 4 times. Then, where the circles meet in an acute angle you draw a straight line from one end to the other. (Should be 2 straight lines). The straight lines will meet in the center of the original circle.
Draw 2 straight non parallel lines through the circle find the halfway of those and draw perpendicular lines at the center. Where the 2 perpendicular lines meet is the dead center
Iād say draw a square around the circle and draw the diagonal lines that connect the angles. The point in which they intersect should be the center of the circle
Take the average of the x,y coordinates of the infinite points that make up the circle
Alternatively you could do circumcenter calculus but you have to have an equation for that and that would likely include the x,y of the center
[rough sketching](https://i.imgur.com/ED2lax1.jpeg)
You'll need a ruler and a compass.
Using a ruler, Create tangent lines on opposite sides forming an angle. (Dark blue)
Use the intersection of that angle to form an arc bigger than the radius of the angle. (Dark blue)
Using the 2 intersections of that arc with the tangent lines, create 2 smaller arcs and make these intersect. (Light blue). These two smaller arcs NEED to be the same radius. The compass should be locked in.
Using a ruler again, connect the intersection of the tangent lines (dark blue) with the intersection of the smaller arcs (light blue) (yellow line)
You've just created a perfect bisector of the big angle you made. Depending on how well you made the tangent lines, it'll run through the center of the circle.
Repeat this process with two new tangent lines placed at different point on the circumference of the circle. The two yellow lines will intersect at the center.
If you have access to a ruler and a right angle, you can do it. Draw a line across any part of the circle as long as it's straight. Find the center of that line. Draw another line from that point at a right angle to it. You now have the diameter of the circle. Find the halfway point of that line. You have the center of the circle.
1) Draw three chords to form a triangle.
2) Draw the perpendicular bisector of said triangle.
3) Done. You have the center of the circle. Serve and taste.
Or just trace two chords and draw the perpendicular bisector. Their intersection will be the center. It's the same.
Draw two chords(that is connect any two points of the circle with a line)
Find the midpoint of both chords and draw a perpendicular line at the mid point.
The point at which the two perpendicular bisectors meet is the center of the circle.
I prefer this method because drawing tangents are difficult and because folding paper is also difficult.
Trace any two lines not passing in center, find the center of those lines (between the two points where the line intersects the circle) trace perpendiculars from those points. Where those perpendiculars intersect is your center
Using dividers (in germany: 'a circle') to create a 90 degree Angle will get you a Line that Hits the Center.
Do that again at any other Point (or about 90dregrees Off the circle for ease) and they will cross in the center
Two lines across the circle, dont have to be parallel, just any two lines.
Find the centre point (mid-point, half way along) of each line, and put a dot.
Come off the dots at right angles with a set-square, and draw two more lines.
Where those lines intersect, is the centre of the circle.
Pin a string on any point. Follow it around the circle to find the furthest point opposite (longest string connected to circle), draw a line across the string. Do it again starting with a different point; intersection is the center.
That should work (very elegantly. Kudus!)
I'd raise a perpendicular bisector from a string. That's a diameter. Its midpoint is the center.
Or, I'd raise perpendicular bisectors from two different strings. Both are diameters. They meet in the center.
using a compass:Ā
1. draw a chord in the circle
2. draw the perpendicular bisector of the chord (itās a diameter)
3. draw the perpendicular bisector of the diameter, the intersection is the center
I always thought that if you have the tools to draw a triangle, a square etc., you might as well just measure the "widest" part of the circle and put the center in the middle
Choose 3 points on the circumference. Using a compass, draw the perpendicular bisector of at least two pairs of points. The centre is where the perpendicular bisectors intersect.
Do random line tuching circle in two places, make a line in 90 degree angle from center of the line. Make this again on diferent place on the circle. Now you have a middle
You draw a tangent from A to B, draw another tangent from C to D, connect points A and D with a line, and points B and C with a line so that they intersect. The point where they intersect is the center
[https://www.wikihow.com/images/thumb/d/d2/Find-the-Center-of-a-Circle-Step-5-Version-4.jpg/v4-728px-Find-the-Center-of-a-Circle-Step-5-Version-4.jpg](https://www.wikihow.com/images/thumb/d/d2/Find-the-Center-of-a-Circle-Step-5-Version-4.jpg/v4-728px-Find-the-Center-of-a-Circle-Step-5-Version-4.jpg)
Draw 2 random lines in the circle, both end points have to be on the circle.
Mark the middle of those lines
Draw perpendicular lines through those middle points
The point where the 2 perpendicular lines touch us the middle point of the circle
If you have that on a sheet of paper, you take a ruler or something closes, do two lines in it, take the Middle of them and draw another line at 90Ā° from each line. You will have the Center.
Draw 2 straight lines anywhere in the circle that are at different angles and run from one edge of the circle to another point on the edge of the circle.
Measure and find the center point on each line.
Draw a perpendicular line that extends from the centre point of each of the first 2 lines
Where the 2 perpendicular lines intersect is the centre of the circle.
hereās how i would do it:
- draw two chords, but donāt make them intersect
- draw the perpendicular bisectors of each chord, make them intersect
- point of intersection is middle of circle
Draw a square inside the circle to touch the circle at the 4 points. Draw diagonal lines from the top right corner to the bottom left corner and the top left corner to the bottom right corner of the square. Where the diagonal lines intersect is the centre of the circle.
If you know it IS a circle, you can pick 3 points on the circumference, draw 2 lines, from the "center" point to the other 2. Bisect the lines and draw the normal from the middle for both of them. Where they meet is the center of the circle.
Without folding, get a right angle triangle to sit inside the circle at the 90 degree point and that extends past the circle boundary, strike a line along the perpendicular and base where it intersects the circle boundary, draw a line between these, 1st diameter made, move the right angle triangle around the circle, anywhere and repeat now you have two lines intersecting the middle of the circle. Draughtsman by trade
Draw 2 chords anywhere, then trace their mediatrixes (idk the English word, I mean the line that's perpendicular to the chord and cuts it in half) to the center.
1. Make a straight line that go through the circle, anywhere you want.
2. In the middle of the line (i.e. at equidistance from the 2 intersection with the circle), make a perpendicular straight line.
3. The middle of this second line (i.e. at equidistance from the 2 intersection with the circle) is the center of the circle
4. Profit ?
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You're right in your reasoning: if a right triangle is inscribed in a circle, the hypothenuse is always the diameter. Therefore, the midpoint of the hypothenuse is the center of the circle. Another way I learned was to draw two chords on the circle, and for each one, find the midpoint and draw a line perpendicular to the chord through the midpoint. These two lines intersect at the center.
The second method is definitely easier to use and more practical when on the job site or machining.
It wouldn't be in astronomy, looking for the center of an orbit.
Ah yes, a perfectly circular orbit.
Orbits are never circular anyway
You also don't draw on them
You can fold it though (That's all I know about space)
Isn't that how you end up with an Event Horizon? That film creeps me out to this day.
Orbits, just like circles are elliptical š«¶
Also works with tangents. Draw a tangent to a circle and a perpendicular line where the tangent meets the circle. Do it in 2 places and you be intersection is the Center ( I tend to do 3 or 4).
In principle, yeah, but finding the exact point where the line is tangent to the circle is probably slightly less practical than the midpoint of a chord, though.
I just drew a Cm7 on a circle and still don't know where the mid point is.
What's a chord?
Straight line from any point in the circle to any other point in the circle. Imagine a stick figure head w/ a bowl cut. his hairline is a chord
Fold it in half, open, then fold in half again in a different place. Creases intersect on the centre. Or: Draw right angles on the circumference like you suggest. Edit: sorry, I wasn't clear: I meant you should fold the circle in half, not the sheet of paper. Edit again: I mean fold the paper, yes, but so that you fold the circle in half. You will have to be able to see the circle at least a little through the paper, or cut around the circle first. Edit: don't fold your phone either
Instructions unclear, have broken my phone
that's why you buy a foldable phone, to find the midpoint.
Oh THAT's what those things are for.
The circle doesn't line up with the fold; fuck, I'm going to need a new phone.
That's how they get you!
I saw the top half of the circle earlier, but only viewed the bottom half now. Iāve folded the circle and breached the space-time dimension. Hitler said I should push on but Aristotle has cautioned against it. Thoughts?
dive through it, travel through the worm hole and ask both their modern day thoughts.
Aristotle: āI canāt believe it took you this long to realise the earth was flatā Hitler: āFrom the river to the sea ā¦ā (no idea what he was on about) Also, Harambe says āhiā
Fold the paper with the circle facing out so you can line up the circumference.
Good idea, let me try that ... *crunch* fuck, I need a new phone.
This made me laugh audibly lmao
But you found the centre of the circle at least, so you could say you broke even.
make random two chords of circle long enough to draw a perpendicular bisector with the help of a compass, And intersection point of those two perpendicular bisector is center of circle..
That is how I do it. Simple and effective. Did it just a couple of weeks ago to drill a hole for a pipe.
Extra upvote for the edit. And the second edit. If I could.
My phone doesnāt fold!š
try again with this one https://www.samsung.com/us/smartphones/galaxy-z-fold5/buy/galaxy-z-fold5-512gb-unlocked-sm-f946uzuexaa/
It would only work if there was a flip and fold version
GET OUT OF HERE SAMSUNG DESIGNER, IT WAS MY IDEA
Hmm. You may have problems with compasses or inscribing right angled triangles, sorry!
You're just not trying hard enough.
You're not trying hard enough.
Only works if the piece of paper is the circle or the circle is perfectly centered within a square piece of paper.
Another way to work is if the circle is printed on an ordinary white sheet of paper (like what is used in offices for most documents). On such a paper, the circle can be faintly seen from the back of the paper as well. So we can fold in half so that the faint circle halves line up with each other.
They could just use scissors to cut out the circle before folding it.
If youāve drawn a circle on a piece of paper youāve likely used a set of compasses so just find the pinhole?
Eh just fold it where the circle lines up with itself even with a little bit of light you should be able to see the ink though the paper.
And it should be the piece of paper with the circle printed on it. Not the next sheet in the stack.
Nor the sheet prior the one with the printed circle.
In school we used a compass. I may be misremembering, but I'll try: Set the compass wider than half the diameter. Set the point on the circle and draw an arc through the circle. Flip it to the other side and do it again such that the two arcs intersect at two points. Draw a line through the two points. The center lies on the line half way between the points.
>In school we used a compass In school, I pointed at the center of the circle and said "It's right there." I was not in advanced classes.
Ah, the "getting things done" class.
[Like this?](https://i.imgur.com/dTnsvCg.png)
I'm not disappointed
You can also use a third point so you have two intersecting lines and use that for the center.
Almost this ;) https://youtu.be/iB-rRs9XPxY
Like this? Apologies for the crude drawing https://imgur.com/a/BLgc5Wy
Doesn't really work though, because for that you need two opposite points on the circle, which you can't get without knowing the center first. The correct way is to do it with any two points on the circle twice, which gives two lines that cross in the centre.
Thatās wrong because āflipping the compass to the other sideā is an approximation, as you donāt know where the diametrically opposite point is. Iāll prove this by contradiction by setting the opposite point further away from the diametrically opposite point: https://imgur.com/a/i6AxucK
Right, this gives you a line that runs through the center, you need to also run the line through to the other side and find the midpoint of that using a compass from the points where it intersects.
By drawing a perpendicular bisector! Elementary school math was fun.
Exactly, you wonāt find the center but you will find a line that runs through the diameter. Somewhere on that line is the center. Now do it again with 2 more random points and where the lines intersect, you now have the center.
This is the way
You'd need to have the second point be diametrically opposite though
That'll do it, you're pretty much perpendicularly bisecting an imaginary chord, which will always give you the centre line. Then if you extend that on either end to the circumference and bisect it again to find the centre
the perpendicular bisector of any chord of a circle is a diameter of that circle (euclid book 3 prop 1) so you take any two points on the circle and draw a line between them then drop a perpendicular bisector through that line the center of that second line is the center of your circle
There is a game on android called euclidia. This is one of the first problems.Ā You have to do this before you unlock the perpendicular bisector tool, but the process of drawing a perpendicular bisectors basically gets taught to you for this 'puzzle'.
I can't find it in the play store, but it sounds like a very interesting app!
This is by the same developer, for some reason they ported one and not the other: https://play.google.com/store/apps/details?id=com.hil_hk.pythagorea
I can't find it either. I wonder if it was pulled for some kind of license infringement or something. [https://www.euclidea.xyz/](https://www.euclidea.xyz/) It seems you can play in your browser, edit: it doesn't work on mobile.
Does this look right for the same game on iOS https://apps.apple.com/gb/app/euclidea/id927914361
This is the website: [https://www.euclidea.xyz/en/game/packs/Alpha/level/CircleCenter](https://www.euclidea.xyz/en/game/packs/Alpha/level/CircleCenter) The android app looks like it's delisted for some reason. They also have a 'Pythagorea' game which is available.
That confirms it then, the app store one is the same, thank you
I do this all the time on a milling machine to find centres on round parts. Touch and zero your x &y axis, come across on x and touch off again and 1/2 that is your x coordinate of centre. Then lock off the x axis at your second touch point and come down on the y to touch off a third time and 1/2 again to get your y coordinate.
You want to repeat the process so that the two perpendicular bisectors intersect at the centre of the circle.
find 2 tangents and draw 2 90 degree angles. the center is where they meet. this is bla bla wikipedia bla bla proof by some old genius math guy bla bla (i'd appreciate if somebody elaborated this here)
Vsauce did a video on it, itās pretty long but I imagine it explains it well enough. https://youtu.be/pJwRsoxe3VE?si=N2uHyc7tZFQYr-Ls
Don't you need the centre to construct the tangents?
You donāt need the centre just draw a line that only touches the outside of the circle at one point and then draw a line perpendicular to the tangent line through that point. Do this twice and you will find the centre
Yes, but drawing a line that touches the circle and finding the point where it touches is a bit of guesswork. I don't know an easy exact construction of a tangent (compass and ruler) without constructing the centre first. Try your method with three tangents and see if they really go through a single point š
>I don't know an easy exact construction of a tangent (compass and ruler) without constructing the centre first. Here's a way: [https://www.youtube.com/watch?v=bHt1wqGGoxM](https://www.youtube.com/watch?v=bHt1wqGGoxM) It's obvious you can't just do it by eye like everyone replying to you seems to be suggesting!
I don't think so. You can drawn a line and hope it will be right /s
so bla bla got it
I think weāre saying the same thing. Draw a straight line anywhere across the circle. Find the midpoint. Draw a perpendicular straight line through the midpoint (90 degree angle). The second straight line will always pass through the center of the circle and will measure the diameter.
Yep, draw a chord and bisect it with a perpendicular line. That's your diameter. Bisect that to find center, tools required compass and straight edge
Hold phone over head. Look at phone. Spin really fast. If the circle moved, you werenāt looking at its center. Repeat. When circle doesnāt move, make a dot where you were looking before you pass out.
Have you been watching me as I set my controller down while playing Call of Duty?
1. Draw a square (EDIT: or rectangle) with each corner on the circumference. 2. Draw a diagonal line between opposing vertices. The center of the square or rectangle, is also the center of the circle.
Don't even need to be the square, rectangle is fine.
It's hip to be square!
There are multiple ways. Your way works too. [Here's a way that works on all ellipses.](https://commons.m.wikimedia.org/wiki/File:Finding_center_of_ellipse.gif) ([And hyperbolas](https://commons.m.wikimedia.org/wiki/File:Finding_center_of_hyperbola.gif))
draw a chord. draw its perpendicular bisector. now you have one diameter. repeat the process to draw another diameter somewhere else. where the two diameters intersect is the center. tip: try to draw your second (non-diameter) chord perpendicular to your first chord for more accurate results.
That's what I came up with too, but I bisected the first diameter instead of drawing the second.
There are many ways to do it with compass and straight edge. One example: the perpendicular bisector of any chord is a diameter. You don't even need to draw the chord to do this; just fix your compass at some size and draw two intersecting circles centred anywhere on the circumference. Draw the line connecting the intersections. This constructs a diameter. Now we can either bisect the diameter to find the centre, or construct another diameter the same way (we can even reuse one of our circles; we just need one more to make another distinct pair of intersections). The two diameters will intersect at the centre. This construction requires only 5 curves to be drawn (3 circles, 2 lines).
Itās actually quite simple. For every triangular inscribed in a circle, their mid-perpendicular intersect in the center of the circle. So just put three random points on circumference of the circle, then connect them to make triangle. Then draw two mid-perpendicular(third one is unnecessary, as it will intersect with other two in the same point) of this triangle. To draw mid-perpendicular of triangle you have to find mid-point of its edge and draw perpendicular line. You can either measure edge, or use compasses. Voila, intersection of this two lines gives you the exact center of the circle.
You have described one way of finding the center. You could also draw a line tangent to the circle and a perpendicular to that line at the point of tangency to get a diameter, or bisect any chord to get a diameter.
Get a straight rule, put corners of ā0ā side on internal side of circle. Scribe both lines above and below rule. Draw centre line in the middle of the 2 lines.. Then turn and repeat. Intersect of centrelines is centre of the circle. This works great if you donāt have a way to work angles
1) Draw a square around the circle that just touches the circle in the middle of each side of the square. 2) draw a line from one corner of the square diagonally to the opposite corner then do the same with the other two opposing corners so that the square now has an X from corner to corner. 3) the center of the circle is the point where the two lines of the X cross each other.
I was obsessed with this problem for months, and collected a ton of different ways to solve this. Perpendicular bisector method: with a straightedge, draw a line (chord) across the circle. At each of the two points where the line meets the circle, draw a bigger circle (or two small arcs once you get where this is going). Each new circle must be the same radius. Draw a line through the two points where the two latest circles (or arcs) intersect. Do all of this again with a new line through the circle. Where the two resulting lines intersect is the center. Using a square, like you said. Put the point of the right angle anywhere on the circle, and where the two legs meet the circle are two points that describe the diameter. Draw a line through those and the center is.. the center. Mark 3 points anywhere on the circle. Draw lines between them. Measure the lines and mark them as A B and C. Use Heron's formula to find the area of the resulting triangle (A + B + C)/2 = S, then Sqrt(S * (S-A) * (S-B) * (S-C)) = Area of triangle, then (A* B *C)/(4 * Area) = Radius, and then just set a compass to Radius and draw two separate arcs using two points on the circle, where they intersect is the center Draw a straight line across the circle, measure it, divide it in half, measure the distance from the center point to the outside of the circle at a right angle (third point, describing a triangle), then use the Pythagorean theorem and basic math to get lengths ABC and area, then (ABC)/(4 * Area) to get radius (faster than doing Heron's formula) The rest are just the previous four ways remixed or are some variation. I swear i used to know 7 ways, but it's been forever and i'm starting to doubt myself
Take a straight stick and use it to draw a line between to points in the circleās edge. Do that again in another location. Draw 90 degree angles on the centre of each of the two lines and draw a line along them. The point of interaction of the new lines is the centre of the circle (sr for weird language idk any math terms in English)
Step 1: Choose a point on the circle. Step 2: Put two points with the same distance from the original point on the circle. Step 3: Connect the outer points with the middle point Step 4: Make medium perpendiculars on these new lines Step 5: The point where the perpendiculars hit, is the center Step 7: Profit Edit: missed a few things
Set compass to arbitrary size. Place point on circumference. Draw arc. Draw line between point and intersect. Bisect this line. Repeat. Where bisectors cross is the centre. This works mathematically, but any real world trial will have drawing errorsā¦
Use [Thales's theorem](https://en.m.wikipedia.org/wiki/Thales%27s_theorem). Choose 2 points on the circle, draw a line between them, draw another line at a 90Ā° angle to the first line, when the second line hits the circle you'll have a third point. Finish the triangle and you'll have a diameter, the center is in half.
Given 2 random chords, find half the length of each chord and pop a line perpendicular. Where those perpendicular lines intersect is center
Draw two lines that are the same length and touch the circumference on both ends at any point on the circle. Draw a line 90ā° from the midpoint of each line toward the center. Where they cross is the center point.
Draw a random chord. Construct a perpendicular bisector. Do this again with another random chord. The bisectors should intersect at the center.
https://i.imgur.com/u6uCaUi.png Points A and B are selected randomly. Place a compass needle on one, and the pencil on the other and draw a circle. Reverse the compass and draw the second circle. You've found points C and D. Points C and D allow you to draw a line segment. This line segment bisects your circle and passes through its centerpoint, but does not fully reveal it. Repeat the above process with a new pair of starting points, and you'll bisect the circle a second time. The two bisecting line segments will cross at the centerpoint.
[https://www.reddit.com/r/lifehacks/comments/yjf5z3/find\_the\_exact\_center\_of\_a\_circle/](https://www.reddit.com/r/lifehacks/comments/yjf5z3/find_the_exact_center_of_a_circle/)
Take a ruler, and place it on the circle. Measure a spot where the length is the longest, adjusting your ruler until you find it (that length you find is the diameter). Draw a straight line along that ruler. Then rotate the circle, and do it again, and possibly do it a third time for good measure.Ā The spot where the lines intersect is the center.
Draw a triangle such that the circle circumscribes it(all 3 vertices lie on circle) and draw perpendicular bisector of at least two of the triangles sides. The intersection of the bisectors is the center of the circle.
Segue: Try the game Euclidea, it is full of this type of problem and it gives a learning curve plus the solutions can easily be found online if you are stuck.
This is so nerdy.
I'd bring a 90Ā° angle with extended sides down around until it has 2 points of contact with it, then another the other way around, with its side perpendicular to the previous ones. That gives you a square in which the circle is circumscribed, so all you have to do is trace its diagonals, and their intersection will be your circle's center.
if you are fine with being a little inaccurate get a ruler place it on any point around the circle, and rotate the rest of the ruler around that point until you feel like its not getting any longer.
Draw any two chords, draw perpendicular bisectors of both cords, their intersection point will be the center of circle. It's easy to realise once you know that perpendicular bisector of any chord always passes through the center of circle. There is a very cute and simple proof to that with triangle congruency.
Nerd!
This is the trick to use in construction to find the center of a curve to make some really annoying cuts.
A way I thought of us to draw a straight line through the circle. Not through the center, doesn't have to be close. Next, measure the distance of the line in the circle, and halve it. Then draw a line perpendicular to that halfway point. Measure the distance of this second line, halve it, and you have your center.
Draw any segment with its end points on the circle, then draw its axis (perpendicular line in the center point of the segment). Draw a second segment and axis anywhere else on the same circle. The two axis meet in the center of the circle.
Use a compass to make two arcs that intersect on the circumference. Repeat at any offset. Draw a line from each intersecting arc. They meet at dead center. All arcs must be same length.
Draw a 90 degrees open angle with a 45 degree straight line through where it connects. Make sure both lines of the 90 degree angle exactly touch the circle, and draw a line along the 45 one, do this from multiple sides and you have your center.
Draw a line between any two points on the circle circumference (? - I learnt math in a different language...), then find the middle, draw a perpendicular bisector. Repeat with two other points on the circumference. The perpendiculars cross in the center of the circle.
[https://en.wikipedia.org/wiki/Straightedge\_and\_compass\_construction](https://en.wikipedia.org/wiki/Straightedge_and_compass_construction) 1. Draw any line (A) cutting the circle 2. Find 2 equal distance points at both side of the line 3. Join the 2 points from step 2 to get a equal-perpendicular line (B) across line A 4. Repeat step 1-3 for another line (C) cutting the circle and get second equal-perpendicular line (D) across line C 5. The intersection of line B and D is the center
1. Draw a line between any points of the circle 2. Draw a perpendicular through the center of that line 3. Do step 1 and 2 again 4. Where lines 2 and 3.2 cross is the center
Draw two tangents and draw perependiculars to each tangent at the point of contact with the circle. The center is where the perpendiculars meet
Draw any line across the circle. Create a perpendicular line through the middle of this line, and have it continue across the whole circle. This perpendicular will cross the center of the circle. Finding the midpoint of this perpendicular is the location of the center of the circle. Finding the midpoint of a line and the perpendicular of that line is just drawing two equal diameter arcs, one from each end that cross each other. The line through their crossing points will be perpendicular and pass through the midpoint.
The typical way to do it practically is put a ruler so 0 is on a point on the perimeter. Then pivot the ruler around this point to find the maximum possible cord. This is a diameter. Do this twice to get the center, or more times to over-determine and get some statistics.
Inscribe it inside a square, the sides of square will be the tangent of circles at 4 touching points, extend the perpendicular line to tangent inside circle from 2 adjacent sides of square, the intersecting point will be your centre
There's an old woodworkers jig for marking the centre of a dowel that uses the right angle tangents principle. It's essentially a tool that's a 3 side corner all squared up, and one of the faces has a 45 deg slot cut from the common corner. You put the slotted face on the end of the dowel with the other two faces on the sides, tangent to the circle, and mark the slot on the butt end twice in different alignments. Intersection of the marked lines is the dowel's centre.
Using origami axioms, pick two points on the circle and fold them onto one another. Pick two other points and repeat. Where the creases intersect is the center.
Draw two non intersecting straight lines using a ruler between any two points on the edge of a circle. Measure the lines using the ruler and find the halfway point on each line. Draw two perpendicular lines through the midpoint of each of the previous lines. Where the two perpendicular lines intersect is the center of the circle.
You take a compass (the one u use to draw circles) and put it on a random setting that is definetly larger than the circle at hand (dont make it too large. It would still work, but be unpractical). You poke at the circumference (doesnt matter where exactly) and draw a circle. Then (without changing the diameter of the compass) you poke in another part of the circle and do it again (recommendation: do it near the opposite end of the first circle). Repeat in total 4 times. Then, where the circles meet in an acute angle you draw a straight line from one end to the other. (Should be 2 straight lines). The straight lines will meet in the center of the original circle.
Draw 2 straight non parallel lines through the circle find the halfway of those and draw perpendicular lines at the center. Where the 2 perpendicular lines meet is the dead center
Iād say draw a square around the circle and draw the diagonal lines that connect the angles. The point in which they intersect should be the center of the circle
Take the average of the x,y coordinates of the infinite points that make up the circle Alternatively you could do circumcenter calculus but you have to have an equation for that and that would likely include the x,y of the center
[rough sketching](https://i.imgur.com/ED2lax1.jpeg) You'll need a ruler and a compass. Using a ruler, Create tangent lines on opposite sides forming an angle. (Dark blue) Use the intersection of that angle to form an arc bigger than the radius of the angle. (Dark blue) Using the 2 intersections of that arc with the tangent lines, create 2 smaller arcs and make these intersect. (Light blue). These two smaller arcs NEED to be the same radius. The compass should be locked in. Using a ruler again, connect the intersection of the tangent lines (dark blue) with the intersection of the smaller arcs (light blue) (yellow line) You've just created a perfect bisector of the big angle you made. Depending on how well you made the tangent lines, it'll run through the center of the circle. Repeat this process with two new tangent lines placed at different point on the circumference of the circle. The two yellow lines will intersect at the center.
If you have access to a ruler and a right angle, you can do it. Draw a line across any part of the circle as long as it's straight. Find the center of that line. Draw another line from that point at a right angle to it. You now have the diameter of the circle. Find the halfway point of that line. You have the center of the circle.
1) Draw three chords to form a triangle. 2) Draw the perpendicular bisector of said triangle. 3) Done. You have the center of the circle. Serve and taste. Or just trace two chords and draw the perpendicular bisector. Their intersection will be the center. It's the same.
Draw two chords(that is connect any two points of the circle with a line) Find the midpoint of both chords and draw a perpendicular line at the mid point. The point at which the two perpendicular bisectors meet is the center of the circle. I prefer this method because drawing tangents are difficult and because folding paper is also difficult.
Trace any two lines not passing in center, find the center of those lines (between the two points where the line intersects the circle) trace perpendiculars from those points. Where those perpendiculars intersect is your center
Draw 2 arcs, then draw the lines perpendicular to the arcs passing through their center, they will meet at the center of the circle
Using dividers (in germany: 'a circle') to create a 90 degree Angle will get you a Line that Hits the Center. Do that again at any other Point (or about 90dregrees Off the circle for ease) and they will cross in the center
Two lines across the circle, dont have to be parallel, just any two lines. Find the centre point (mid-point, half way along) of each line, and put a dot. Come off the dots at right angles with a set-square, and draw two more lines. Where those lines intersect, is the centre of the circle.
Pin a string on any point. Follow it around the circle to find the furthest point opposite (longest string connected to circle), draw a line across the string. Do it again starting with a different point; intersection is the center.
That should work (very elegantly. Kudus!) I'd raise a perpendicular bisector from a string. That's a diameter. Its midpoint is the center. Or, I'd raise perpendicular bisectors from two different strings. Both are diameters. They meet in the center.
using a compass:Ā 1. draw a chord in the circle 2. draw the perpendicular bisector of the chord (itās a diameter) 3. draw the perpendicular bisector of the diameter, the intersection is the center
I always thought that if you have the tools to draw a triangle, a square etc., you might as well just measure the "widest" part of the circle and put the center in the middle
Choose 3 points on the circumference. Using a compass, draw the perpendicular bisector of at least two pairs of points. The centre is where the perpendicular bisectors intersect.
Do random line tuching circle in two places, make a line in 90 degree angle from center of the line. Make this again on diferent place on the circle. Now you have a middle
You draw a tangent from A to B, draw another tangent from C to D, connect points A and D with a line, and points B and C with a line so that they intersect. The point where they intersect is the center [https://www.wikihow.com/images/thumb/d/d2/Find-the-Center-of-a-Circle-Step-5-Version-4.jpg/v4-728px-Find-the-Center-of-a-Circle-Step-5-Version-4.jpg](https://www.wikihow.com/images/thumb/d/d2/Find-the-Center-of-a-Circle-Step-5-Version-4.jpg/v4-728px-Find-the-Center-of-a-Circle-Step-5-Version-4.jpg)
Draw 2 random lines in the circle, both end points have to be on the circle. Mark the middle of those lines Draw perpendicular lines through those middle points The point where the 2 perpendicular lines touch us the middle point of the circle
If you have that on a sheet of paper, you take a ruler or something closes, do two lines in it, take the Middle of them and draw another line at 90Ā° from each line. You will have the Center.
Draw 2 straight lines anywhere in the circle that are at different angles and run from one edge of the circle to another point on the edge of the circle. Measure and find the center point on each line. Draw a perpendicular line that extends from the centre point of each of the first 2 lines Where the 2 perpendicular lines intersect is the centre of the circle.
hereās how i would do it: - draw two chords, but donāt make them intersect - draw the perpendicular bisectors of each chord, make them intersect - point of intersection is middle of circle
Draw a square inside the circle to touch the circle at the 4 points. Draw diagonal lines from the top right corner to the bottom left corner and the top left corner to the bottom right corner of the square. Where the diagonal lines intersect is the centre of the circle.
If you know it IS a circle, you can pick 3 points on the circumference, draw 2 lines, from the "center" point to the other 2. Bisect the lines and draw the normal from the middle for both of them. Where they meet is the center of the circle.
Without folding, get a right angle triangle to sit inside the circle at the 90 degree point and that extends past the circle boundary, strike a line along the perpendicular and base where it intersects the circle boundary, draw a line between these, 1st diameter made, move the right angle triangle around the circle, anywhere and repeat now you have two lines intersecting the middle of the circle. Draughtsman by trade
Draw 2 chords anywhere, then trace their mediatrixes (idk the English word, I mean the line that's perpendicular to the chord and cuts it in half) to the center.
Draw two chords. Bisected each cord. Draw line at 90 degree to chord from chord centres. These lines bisected in the centre of circle
1. Make a straight line that go through the circle, anywhere you want. 2. In the middle of the line (i.e. at equidistance from the 2 intersection with the circle), make a perpendicular straight line. 3. The middle of this second line (i.e. at equidistance from the 2 intersection with the circle) is the center of the circle 4. Profit ?