Prove that the perpendicular bisectors of the sides of a cyclic quadri

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

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

Answer»

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

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

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