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