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concyclic, starting with an inscribed pentagon

Source: KJMO 2012 p2

May 3, 2019
geometrypentagonConcyclic

Problem Statement

A pentagon ABCDEABCDE is inscribed in a circle OO, and satis fies ∠A=90o,AB=CD\angle A = 90^o, AB = CD. Let FF be a point on segment AEAE. Let BFBF hit OO again at J(≠B)J(\ne B), CE∩DJ=KCE \cap DJ = K, BD∩FK=LBD\cap FK = L. Prove that B,L,E,FB,L,E,F are cyclic.
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