Q. 193.9( 7 Votes )

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

Answer :

Let, ABCD be a cyclic quadrilateral and O be the center of

the circle passing through A, B, C, and D.

Then,

Each of AB, BC, CD and DA being a chord of the

circle, its right bisector must pass through O.

Therefore,

The right bisectors of AB, BC, CD and DA pass through and are concurrent.

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