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Angle equality in cyclic quadrilateral

Source:

July 22, 2012
invariantgeometrycyclic quadrilateralradical axispower of a pointgeometry proposed

Problem Statement

The cirumcentre of the cyclic quadrilateral ABCDABCD is OO. The second intersection point of the circles ABOABO and CDOCDO, other than OO, is PP, which lies in the interior of the triangle DAODAO. Choose a point QQ on the extension of OPOP beyond PP, and a point RR on the extension of OPOP beyond OO. Prove that ∠QAP=∠OBR\angle QAP=\angle OBR if and only if ∠PDQ=∠RCO\angle PDQ=\angle RCO.
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