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pure geometry-prove

Source:

February 22, 2015
geometryincentersymmetrygeometry unsolved

Problem Statement

A circle ω\omega through the incentreI I of a triangle ABCABC and tangent to ABAB at AA, intersects the segment BCBC at DD and the extension ofBC BC at EE. Prove that the line ICIC intersects ω\omega at a point MM such that MD=MEMD=ME.
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