MathDB
Altitude and Midpoints

Source: 2016 Taiwan TST Round 3

July 25, 2016
geometry

Problem Statement

Let ABCABC be an acute-angled triangle, with ∠B≠∠C\angle B \neq \angle C . Let MM be the midpoint of side BCBC, and E,FE,F be the feet of the altitude from B,CB,C respectively. Denote by K,LK,L the midpoints of segments ME,MFME,MF, respectively. Suppose TT is a point on the line KLKL such that AT//BCAT//BC. Prove that TA=TMTA=TM .
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