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(con)cyclic wanted, symmetrics wrt sides

Source: 2015 Saudi Arabia Pre-TST 1.1

September 12, 2020
geometrySymmetriccyclic quadrilateralConcyclic

Problem Statement

Let ABCABC be a triangle and DD a point on the side BCBC. Point EE is the symmetric of DD with respect to ABAB. Point FF is the symmetric of EE with respect to ACAC. Point PP is the intersection of line DFDF with line ACAC. Prove that the quadrilateral AEDPAEDP is cyclic.
(Malik Talbi)
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