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 be the center of the circle. Draw , a chord  and let be its midpoint. Construct perpendicular to latex R as shown above. We show that is on .
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…