Question 174
Let $ABC$ be a triangle with $AB \neq AC$. The incircle of triangle $ABC$ is tangent to $BC$, $CA$, $AB$ at $D$, $E$, $F$, respectively. The perpendicular line from $D$ to $EF$ intersects $AB$ at $X$. The second intersection point of circumcircles of triangles $AEF$ and $ABC$ is $T$. Prove that $TX \perp TF$.