If two circles intersect at two points, prove that their centres lie on the perpendicular

bisector of the common chord. Please help me.

If two circles intersect at two points, prove that their centres lie on the perpendicular

bisector of the common chord. Please help me.

bisector of the common chord. Please help me.

What have you tried? You drew the circles; labeled the chord's endpoints (say, A and B), the circles' centers (say, P and Q); drew the segments AB and PQ; and labelled their intersection point (say, M).If two circles intersect at two points, prove that their centres lie on the perpendicular

bisector of the common chord. Please help me.

I don't know what theorems you have to work with (geometry books get to different theorems in different orders), but what can you say about the triangles PAQ, PBQ, angles APM and BPM, etc?

If you get stuck, please reply telling what you've tried and how far you got. Thanks.