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Geo the great

Source: RMM Shortlist 2023 G2

February 29, 2024
cyclic quadrilateralRMM ShortlistgeometryHybrid

Problem Statement

Let ABCDABCD be a cyclic quadrilateral. Let DADA and BCBC intersect at EE and let ABAB and CDCD intersect at FF. Assume that A,E,FA, E, F all lie on the same side of BDBD. Let PP be on segment DADA such that ∠CPD=∠CBP\angle CPD = \angle CBP, and let QQ be on segment CDCD such that ∠DQA=∠QBA\angle DQA = \angle QBA. Let ACAC and PQPQ meet at XX. Prove that, if EX=EPEX = EP, then EFEF is perpendicular to ACAC.
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