How to reconstruct a full circle from an arc
When given a piece of a circle, called an arc (or even three points on a circle, two chords, etc.) it is possible to reconstruct the entire circle by finding the center. In this video I demonstrate that the perpendicular bisector of a chord always passes through the center of the circle, allowing us to find the center by forming two chords and constructing their perpendicular bisectors. I then demonstrate a proof that the perpendicular bisector of a chord will always pass through the center of a circle. This proof relies on showing that the line joining the midpoint of the chord to the center of the circle is perpendicular to the chord. This result follows from demonstrating that the triangles formed by joining the center to the midpoint and endpoints of the chord are congruent.