Problem

Source: Turkey JBMO TST 2023 Day 2 P3

Tags: geometry, tangent



Let $ABC$ is triangle and $D \in AB$,$E \in AC$ such that $DE//BC$. Let $(ABC)$ meets with $(BDE)$ and $(CDE)$ at the second time $K,L$ respectively. $BK$ and $CL$ intersect at $T$. Prove that $TA$ is tangent to the $(ABC)$