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