Question

Question 9
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.

Answer 1

True

We drew two circles with centres $C_1$ and $C_2$ passing through the end points P and Q of a line segment PQ.
We know, that perpendicular bisector of a chord of a circle always, passes through the centre of the circle.
Thus, the perpendicular bisector of PQ passes through $C_1$ and $C_2$.
Similarly, all the circle passing through PQ will have their centre on perpendicular bisectors of PQ.