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Show that D, C, K, L lie on a circle

Source: Turkey National Olympiad 2006 - D1 - P1

January 6, 2007
geometrycircumcirclepower of a pointradical axiscyclic quadrilateralgeometry unsolved

Problem Statement

Points PP and QQ on side ABAB of a convex quadrilateral ABCDABCD are given such that AP=BQ.AP = BQ. The circumcircles of triangles APDAPD and BQDBQD meet again at KK and those of APCAPC and BQCBQC meet again at LL. Show that the points D,C,K,LD,C,K,L lie on a circle.
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