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.

पर्याय

• 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.