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Incircle geometry

Source: Bosnia and Herzegovina TST 2015 day 2 problem 3

May 18, 2015
geometryincircleincenterperpendicular bisectorparallel

Problem Statement

Let DD, EE and FF be points in which incircle of triangle ABCABC touches sides BCBC, CACA and ABAB, respectively, and let II be a center of that circle.Furthermore, let PP be a foot of perpendicular from point II to line ADAD, and let MM be midpoint of DEDE. If {N}=PM∩AC\{N\}=PM\cap{AC}, prove that DN∥EFDN \parallel EF
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