Prove that the perpendicular bisector of a chord passes through the centre of the circle. Class 9

Prove that the perpendicular bisector of a chord passes through the centre of the circle. Class 9

Question 1.

Prove that the perpendicular bisector of a chord passes through the centre of the circle. Class 9

Solution:

Given: AB is a chord of a circle with centre O.

MN is the perpendicular bisector of AB.

To prove: O lies on the perpendicular bisector of AB.

OA = OB = r ..[radii of the same circle]

∴ O is equidistant from A and B.

Since, any point equidistant from two points lies on the perpendicular bisector of the segment joining them.

∴ O lies on the perpendicular bisector of AB.

∴ The perpendicular bisector of any chord passes through the centre.