Question

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

Answer 1

Two circles with centre A and B intersect at ‘C’ and ‘D’. 

CD is the common chord for these circles. 

To Prove: A and B centres are on bisector of CD. 

Proof: Circle with centre ‘A’. 

CD is the chord. CD meets B through ‘O’. 

CD is the chord for circle centred B.

Now CD meet A through ‘O’. 

Hence, If two circles intersect at two points, their centres lie on the perpendicular bisector of the common chord.