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<MTW=<TLM wanted, incircle, median, angle bisector, altitude related

Source: Germany Federal - Bundeswettbewerb Mathematik 2019 round 2, p3

April 16, 2020
geometryequal anglesincircle

Problem Statement

Let ABCABC be atriangle with AC‾>BC‾\overline{AC}> \overline{BC} and incircle kk. Let M,W,LM,W,L be the intersections of the median, angle bisector and altitude from point CC respectively. The tangent to kk passing through MM, that is different from ABAB, touch kk in TT. Prove that the angles ∠MTW\angle MTW and ∠TLM\angle TLM are equal.
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