prove that the perpendicular bisector of the sides of a cyclic quadrilateral are concurrent.
Let ABCD be the cyclic quadrilateral and PO, QO, RO and SO be the perpendicular bisectors of side AB, BC, CD and AD.
We know that perpendicular bisector of a line segment passes through the centre.
⇒ PO, QO, RO and SO passes through centre.
⇒ PO, QO, RO and SO are concurrent.
Hence the perpendicular bisector of a sides of cyclic quadrilateral are concurrent.