Question

Prove that the common chord of two intersecting circles is bisected at right angles by the line of centres.

Answer 1

Given two intersecting circles with center $C$ and $D$ and $AB$ is the common chord.

Then, $CA=CB$ ...... (Radius of circle)

So, $C$ lies on the right bisector $AB$

And $AD=BD$ ......... (Radius of circle)

So, $D$ lies on the right bisector of $AB$.

Thus, $CD$ is the bisector of $AB$

Then, the common chord bisected at right angle by the line joining the centres.