Q : 3 If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.
Given: Two circles intersect at two points.
To prove: their centres lie on the perpendicular bisector of the common chord.
Construction: Joinpoint P and Q to midpoint M of chord AB.
Proof: AB is a chord of circle C(Q,r) and QM is the bisector of chord AB.
Hence,
Similarly, AB is a chord of circle(Q,r' ) and QM is the bisector of chord AB.
Hence,
Now,
PMA and QMA are forming linear pairs so PMQ is a straight line.
Hence, P and Q lie on the perpendicular bisector of common chord AB.