Question 86
Let $I$ be the incenter of the acute-angled non-isosceles triangle $ABC$. Let the incircle touch the side $AB$ at point $Q$. Point $T$ is marked on the side $AB$ so that $IT \parallel CQ$. The line through $T$ touches the incircle at point $K$ (different from $Q$) and meets the lines $CA$ and $CB$ at points $L$ and $N$, respectively.
Prove that $T$ is the midpoint of the segment $LN$.
(Ya. Konstantinovski)
Prove that $T$ is the midpoint of the segment $LN$.
(Ya. Konstantinovski)