Question 8
$\triangle ABC$ is a triangle with $AB \lt BC$, $\mathcal{C}$ its circumcircle, $K$ the midpoint of the minor arc $\widehat{CA}$ of the circle $\mathcal{C}$ and $T$ a point on $\mathcal{C}$ such that $KT$ is perpendicular to $BC$. If $A'$, $B'$ are the intouch points of the incircle of $\triangle ABC$ with the sides $BC$, $AC$, prove that the lines $AT$, $BK$, $A'B'$ are concurrent.