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Perpendicular diagonals in cyclic quadrilateral

Source: 2014 China TST 1 Day 1 Q1

March 18, 2014
geometrycyclic quadrilateralperpendicular bisector

Problem Statement

ABCDABCD is a cyclic quadrilateral, with diagonals AC,BDAC,BD perpendicular to each other. Let point FF be on side BCBC, the parallel line EFEF to ACAC intersect ABAB at point EE, line FGFG parallel to BDBD intersect CDCD at GG. Let the projection of EE onto CDCD be PP, projection of FF onto DADA be QQ, projection of GG onto ABAB be RR. Prove that QFQF bisects ∠PQR\angle PQR.
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