Pls tell how to prove his question .
Prove the the perpendicular bisector of a chord of a circle passes through the centre of the circle.
Let t AB be the chord of the circle with centre O. and PQ be its perpendicular bisector.
If PQ does not pass through the centre O, join O to the mid-point M of the chord AB.
Then, [straight line joining the centre to the mid-point of the chord is perpendicular to the chord]
But [given MP is perpendicular bisector of AB]
Therefore, which is possible only if the OM coincide with the perpendicular bisector of AB.
Hence PQ must pass through the centre O.