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Prove Points are Concyclic

Source: 2017 Greece National Olympiad Problem 1

May 2, 2017
geometryTrianglecyclic quadrilateralConcyclic

Problem Statement

An acute triangle ABCABC with AB<AC<BCAB<AC<BC is inscribed in a circle c(O,R)c(O,R). The circle c1(A,AC)c_1(A,AC) intersects the circle cc at point DD and intersects CBCB at EE. If the line AEAE intersects cc at FF and GG lies in BCBC such that EB=BGEB=BG, prove that F,E,D,GF,E,D,G are concyclic.
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