Problem 359. Cyclic quadrilateral, Angle bisector, Rhombus.
Level: High School, College, SAT Prep. In the figure below, ABCD is a cyclic quadrilateral. Lines AB and DC meet at E, and lines AD and BC meet at F. The bisectors of angles AED and AFB meet the sides BC, AD, CD, and AB at points M, N, G, and H, respectively. Prove that HMGN is a rhombus.

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