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Concyclic points

Source: Iberoamerican Olympiad 1990, Problem 4

May 18, 2007
geometryincenterpower of a pointgeometry proposed

Problem Statement

Let ABCABC be a triangle. II is the incenter, and the incircle is tangent to BCBC, CACA, ABAB at DD, EE, FF, respectively. PP is the second point of intersection of ADAD and the incircle. If MM is the midpoint of EFEF, show that PP, II, MM, DD are concyclic.
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