Question

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

Options

• True

• False

Answer 1

This statement is True.

Explanation:

We draw two circle with centre C₁ and C₂ passing  through the endpoint P and Q at a line segment PQ.

We know, that perpendicular bisectors of a chord of a circle always passes through the centre of circle.

Thus, perpendicular bisector of PQ passes through C1 and C2.

Similarly, all the circle passing through PQ will have their centre on perpendiculars bisectors of PQ.