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Prove that the perpendicular bisector...

Prove that the perpendicular bisectors of the sides of a cyclic quadrilateral are concurrent.

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Let ABCD be a cyclic quadrilateral and let O be the centre of the centre , passing through A,B,C,D. Then , each of AB, BC, CD and DA being a chord of the circle, its right bisector must pass through O .Hence, the right bisectors of AB, BC ,CD and DA pass through O .
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