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Paralell lines and tangent to (ABC)

Source: Turkey JBMO TST 2023 Day 2 P3

April 30, 2023
geometrytangent

Problem Statement

Let ABCABC is triangle and D∈ABD \in AB,E∈ACE \in AC such that DE//BCDE//BC. Let (ABC)(ABC) meets with (BDE)(BDE) and (CDE)(CDE) at the second time K,LK,L respectively. BKBK and CLCL intersect at TT. Prove that TATA is tangent to the (ABC)(ABC)
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