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.

perpendicular bisector

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.

Perpendicular Bisector


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