prove that the perpendicular bisector of the sides of cyclic quadrilateral are concurrent
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Let ABCD be the cyclic quadrilateral.
Let OL, OM, ON and OP be the perpendicular bisectors of sides AB, BC, CD and AD respectively.
Recall that perpendicular bisector of a line segment passes through the centre of the circle.
Hence OL, OM, ON and OP pass through the centre.
⇒ OL, OM, ON and OP are concurrent.
Thus the perpendicular bisectors of sides of cyclic quadrilateral are concurrent.
Let OL, OM, ON and OP be the perpendicular bisectors of sides AB, BC, CD and AD respectively.
Recall that perpendicular bisector of a line segment passes through the centre of the circle.
Hence OL, OM, ON and OP pass through the centre.
⇒ OL, OM, ON and OP are concurrent.
Thus the perpendicular bisectors of sides of cyclic quadrilateral are concurrent.
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