Pls tell how to prove his question Prove the the perpendicular bisector of a chord of a - Maths - Circles

Question

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

Varun Rawat · Accepted Answer

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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

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.

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.