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4 concylic points

Source: Swiss Math Olympiad 2010 - final round, problem 2

March 16, 2010
geometrygeometry proposed

Problem Statement

Let △ABC \triangle{ABC} be a triangle with AB\not\equal{}AC. The incircle with centre I I touches BC BC, CA CA, AB AB at D D, E E, F F, respectively. Furthermore let M M the midpoint of EF EF and AD AD intersect the incircle at P\not\equal{}D. Show that PMID PMID ist cyclic.
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