We start with a given circle.

Geometry construction with compass and straightedge or ruler or ruler
1.  Place the right-angle corner of any object at any point on the circle. Any point will do. Geometry construction with compass and straightedge or ruler or ruler
2.  Make a mark where the two sides of the right-angle cross the circle. Geometry construction with compass and straightedge or ruler or ruler
3.  Draw a line between these two marks. Because of Thales Theorem, this is a diameter of the circle. Geometry construction with compass and straightedge or ruler or ruler
4.  Place the right-angle corner of the object at any other point on the circle. Any point will do, but for greatest accuracy, make it about a quarter the way round the circle from the first point. Geometry construction with compass and straightedge or ruler or ruler
5.  Make a mark where the two sides of the right-angle cross the circle. Geometry construction with compass and straightedge or ruler or ruler
6.  Connect these two points with a straight line. This is the second diameter. Geometry construction with compass and straightedge or ruler or ruler
7.  Done. The point where the two diameters intersect is the center of the circle. Geometry construction with compass and straightedge or ruler or ruler

Why it works

Geometry construction with compass and straightedge or ruler or rulerThis method works as a result of Thales Theorem. The diameter of a circle subtends a right angle to any point on the circle. The converse is also true: A right angle on the circle must cut off a diameter. By finding two diameters, we find the center where they intersect

Visit Thales Theorem for an animated description of how this works.

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This just solved a problem I was anticipating I would run into later. Now I know how to avoid it.

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