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China 2017 TSTST1 Day 2 Geometry Problem

Source: China 2017 TSTST1 Day 2 Problem 5

March 7, 2017
geometry

Problem Statement

In the non-isosceles triangle ABCABC,DD is the midpoint of side BCBC,EE is the midpoint of side CACA,FF is the midpoint of side ABAB.The line(different from line BCBC) that is tangent to the inscribed circle of triangle ABCABC and passing through point DD intersect line EFEF at XX.Define Y,ZY,Z similarly.Prove that X,Y,ZX,Y,Z are collinear.
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