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Line DT tangent to incircle

Source: 2020 Korean MO winter camp Test 1 P4

September 7, 2020
geometry

Problem Statement

II is the incenter of a given triangle △ABC\triangle ABC. The angle bisectors of ABCABC meet the sides at D,E,FD,E,F, and EFEF meets (ABC)(ABC) at LL and TT (FF is on segment LELE.). Suppose MM is the midpoint of BCBC. Prove that if DTDT is tangent to the incircle of ABCABC, then ILIL bisects ∠MLT\angle MLT.
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