# The Perpendicular Bisector of A Chord Passes The Center of a Circle

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

# Proving the Perpendicular Bisector Theorem Using SAS Congruence

In the previous post, we have proved the Perpendicular Bisector Theorem using reflection. In this post, we prove the same theorem using SAS Congruence.

Theorem

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. Continue reading