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Cute angle chasing problem

Source: Sharygin Finals 2022 9.5

August 1, 2022
geometry

Problem Statement

Chords ABAB and CDCD of a circle ω\omega meet at point EE in such a way that AD=AE=EBAD = AE = EB. Let FF be a point of segment CECE such that ED=CFED = CF. The bisector of angle AFCAFC meets an arc DACDAC at point PP. Prove that AA, EE, FF, and PP are concyclic.
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