Question

If a number of circles pass through the end points P and Q of a line segment PQ, then their centres lie on the perpendicular bisector of ______.

Answer 1

If a number of circles pass through the end points P and Q of a line segment PQ, then their centres lie on the perpendicular bisector of PQ.

Explanation:

For any circle through P and Q the segment PQ is a chord and the perpendicular bisector of a chord passes through the circle’s centre (so CP = CQ and C lies on that bisector). 

Hence every such circle’s centre lies on the perpendicular bisector of PQ.