Question

if two circles intersect at two point prove that their centres lie on the perpendicular bisector on the common chord

Answer 1

Answer:

Figure shows two circles intersect at A and B, AB is common chord. P and Q are centres of circles.

Let C is mid point of AB. let us join PC and QC.

In a circle, line drawn from centre of circle to the mid point of chord is perpendicular to that chord.

hence PC is perpendicular to AB and QC is perpendicular to AB.