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Question

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

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Solution

Given: ABCD is a cyclic quadrilateral.

To prove: The perpendicular bisectors of the sides are concurrent.

Proof: Each side of the cyclic quadrilateral is a chord of the circle and perpendicular bisector of a chord passes through the centre of the circle.

The perpendicular bisectors of each side will pass through the centre O.

Hence, the perpendicular bisectors of the sides of a cyclic quadrilateral are concurrent.


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