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