#2 Midpoint of circle

You come into a room and see that someone has drawn a perfect circle on a paper. Beside it you see a long ruler, on which all the markings has unfortunately decayed, and a big compassA drawing tool for making circles. You are curious as to how they drew such a perfect circle. Can you use the compass and ruler to find where exactly the center of the circle lies?

look into this: straight edge and compass construction

Yes you can! The steps used to find the exact midpoint are shown in the figma slides below.

A relevant theorem is the perpendicular bisector of chord theoremthe perpendicular bisector of a chord passes through the center of the circle.