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, AMO =90     [straight line joining the centre to the mid-point of the chord is perpendicular to the chord]

But AMP=90      [given MP is perpendicular bisector of AB]

Therefore,  AMO=AMP which is possible only if the OM coincide with the perpendicular bisector of AB.

Hence PQ must pass through the centre O.

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