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Prove that the perpendicular bisectors of the sides of a cyclic quadrilateral are concurrent.
To do:
We have to prove that the perpendicular bisectors of the sides of a cyclic quadrilateral are concurrent.
Solution:
Let $ABCD$ is a cyclic quadrilateral.
We know that,
Each side of the cyclic quadrilateral is a chord of the circle and the perpendicular of a chord passes through the centre of the circle.
Therefore,
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.
Updated on: 10-Oct-2022
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