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Nine point circle is tangent to incircle and three excircles

Source: China TST 2011 Day 1

March 28, 2011
geometryrectangleanalytic geometrytrapezoidgeometric transformationhomothetytrigonometry

Problem Statement

In △ABC\triangle ABC we have BC>CA>ABBC>CA>AB. The nine point circle is tangent to the incircle, AA-excircle, BB-excircle and CC-excircle at the points T,TA,TB,TCT,T_A,T_B,T_C respectively. Prove that the segments TTBTT_B and lines TATCT_AT_C intersect each other.
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