The perpendicular bisector of a chord of a circle passes through its center. In this post, we prove this claim.

Let $latex O$ be the center of the circle. Draw $latex \overline{PQ}$, a chord  and let $latex R$ be its midpoint.

Construct $latex \overline{ST}$ perpendicular to $latex \overline{PQ} at $latex R as shown above. We show that $latex O$ is on $latex \overline{ST}$. Continue reading →