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The figure shows the circumcircle of a triangle ABC with the altitudes AD, BE, and CF. EF extended cuts arc AB at M. Lines BM and DF meet at N. Prove that (1) AFMN is a cyclic quadrilateral; (2) AM = AN. This entry contributed by Peter Tran.

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Post or view a solution to the problem 1213 Last updated: May 11, 2016