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three points are collinear

Source: China south east mathematical Olympiad 2008 day2 problem 6

July 15, 2013
geometrytrigonometrygeometry unsolved

Problem Statement

Circle II is the incircle of △ABC\triangle ABC. Circle II is tangent to sides BCBC and ACAC at M,NM,N respectively. E,FE,F are midpoints of sides ABAB and ACAC respectively. Lines EF,BIEF, BI intersect at DD. Show that M,N,DM,N,D are collinear.
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