If two circles intersect at two points, then prove that their centres lie on the perpendicular bisector of the common chord

Let two circles with centres O and P intersecting each other at A and B.

**To prove** OP is the perpendicular bisector of common chord AB.

**Construction** Join OA, OB, BP and PA. Let OP intersects AB at M.

Hence, OP is the perpendicular bisector of AB.