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Easy Geometry

Source: 2015 Korean Mathematical Olympiad P2

November 1, 2015
geometrycircumcircle

Problem Statement

Let the circumcircle of △ABC\triangle ABC be ω\omega. A point DD lies on segment BCBC, and EE lies on segment ADAD. Let ray AD∩ω=FAD \cap \omega = F. A point MM, which lies on ω\omega, bisects AFAF and it is on the other side of CC with respect to AFAF. Ray ME∩ω=GME \cap \omega = G, ray GD∩ω=HGD \cap \omega = H, and MH∩AD=KMH \cap AD = K. Prove that B,E,C,KB, E, C, K are cyclic.
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