How To Find The Center Of A Circle Using A Square

Thales' Theorem is a great way to find the center of a circle using just a square and a writing instrument. I'll also show you how you can prove this theorem to be true.

[prh]

Well done and thank you! As a retired high school math teacher I loved your geometry! Technically you proved that "if an angle is inscribed in a semicircle, then it is a right angle." What is really needed is the converse statement, "if a right angle is inscribed in a circle, then the endpoints of the chords form a diameter." The proof of that converse statement is actually much easier than the one that you did. (A true statement does not automatically guarantee a true converse. They both require independent proofs.) But enough of that! Please forgive me for the math lesson. But I really enjoyed it!!! ;-)

[Downhaven]

I love these videos Ben.
But after you teach them they're generally so simple that I'm ashamed of the ignorance beforehand.

As always, thank you for sharing. You're an incredible teacher and I am grateful you continue to do so.

[willb]

You brought back a lot memories....and offered a lot of useful tips today.. Geometry was the only math class I ever actually liked and at least for me, beyond the basic add/subtract/multiply/divide, the most useful.

[craigmooring]

Now, if you only have a ruled straight-edge, you can draw any 2 chords* and mark the midpoint of each. From each end of one chord draw an arc with the same radius ( greater than 1/2 of the chord, but the longer the better) so that the arcs intersect inside the circle. Connect the midpoint of the chord to the arc intersection with a straight line and extend that line if necessary to be clearly closer to the opposite side of the circle. Repeat with the other chord. Those two lines intersect at the center of the circle and each of them is perpendicular to their chord as well as coinciding with a diameter of the circle.

*A chord is a straight line segment whose ends are also on the circumference of a circle.

[knifetex]

Yes sir! Done many a shade tree fab job laying out like that. That geometry lesson at the end took me back 30 years to HS!

[johnmatchett]

Brilliantly simple. I've tried a few of these techniques for finding a circle centre and this is probably the best. The beauty is that any piece of A4/letter paper with a square cut edge works: you don't even need a proper 'square'.

JM

[iamarawn]

This is amazing. I learned something new today. I always used rulers to find it by keeping the edge fixed and moving the inner one. This is way easier

[michellemartin]

I loved that you added the math at the end. I was working on a quick project, but stuck around to learn more about it. Thank you!

[moorwaldent]

Smart clips!!! I just learned a lot here. Thank you very much!

[rottnlove]

This will always be the easiest method to find the center of a circle. No measuring and anything that has a sharp pointed corner like sheet of paper or a book can be used

[thepeel]

Nobody’s going to mention how good that freehand circle was?

[Ffan]

I do templates as part of my job and love these videos. Big time savers!

[mingshey]

Great instruction video. If anybody objects you just turn the disk about the marked point on a lathe and scrape off the circumference.

[arzelaascoli]

Is it not the converse that you need to show (that is, you have to show that if you inscribe a right triangle in a circle, its hypotenuse is a diameter: you showed if one side of an inscribed triangle is a diameter, it is a right triangle)?

[elkanahgray]

Another method: draw a line segment having two point (point c1 and point c2) anywhere on the circumference of the circle. then draw a perpendicular line with three points: points d1 and d2 on the circumference, and point d3 being the midpoint of line segment c1 to c2. Therefore, the center of the circle is the midpoint of line segment d1 to d2. Why: because line segment c1 to c2 is parallel with a tangent line of the circle, and all tangent lines are perpendicular to the diameter of the circle

[RockSleeper]

you could just measure the mid-point of the hypotenuse of the first triangle. or you could just draw a line anywhere on the circle through 2 points of the edge of the circle. Then find the midpoint of that line, use the square to make a perpendicular line from the that midpoint, through 2 points of the circle, that gives you the diameter, then find the midpoint of that line for the center of the circle.

[kooper]

There are many other ways but this method is almost unique to metal workers as it is the way to find centre with a 90° rule.

[johnnyrevere]

More great helpful tips..thanks TOOL Crib you a good fella

[Must_not_say_that]

Why not just use dividers? Set them at the maximum width of the circle and there yoiu have the diameter. Simply halve.

[stephenfloodphoto]

Really enjoying your content...if you don't mind sharing, what is your background and/or what do you do for a living?