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Convex Quadrilateral with Bisector Diagonal

Source: Germany TST 2017

April 11, 2020
geometry

Problem Statement

In a convex quadrilateral ABCDABCD, BDBD is the angle bisector of ∠ABC\angle{ABC}. The circumcircle of ABCABC intersects CD,ADCD,AD in P,QP,Q respectively and the line through DD parallel to ACAC cuts AB,ACAB,AC in R,SR,S respectively. Prove that point P,Q,R,SP,Q,R,S lie on a circle.
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