Question

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

Answer 1

Let ABCD be a cyclic quadrilateral, and let O be the center of the corresponding circle Then, each side of the equilateral ABCD is a chord of the circle and the perpendicular bisector of a chord always passes through the center of the circle 

So, right bisectors of the sides of quadrilaterals ABCD, will pass through the circle O of the corresponding circle