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

Consider two circles with centres O₁ and O₂ passing through the end points P and Q of a line segment PQ.



We know that the perpendicular bisector of the chord of a circle passes through the centre of the circle.

Thus, the perpendicular bisector PQ passes through the centres O₁ and O₂.

In the same manner, all circles passing through the end points P and Q of a line segment PQ will have their centres lying on the perpendicular bisector of PQ.


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___.