Question 86
Let $D$, $E$ and $F$ be the contact points of the incircle of $\triangle ABC$ with sides $BC$, $CA$ and $AB$ respectively. Let $I$ and $I'$ be the incentres of $\triangle ABC$ and $\triangle DEF$, respectively. Let $\ell_A$ be the line passing through $D$ and is parallel to $AI'$, $\ell_B$ be the line passing through $E$ and is parallel to $BI'$, and $\ell_C$ be the line passing through $F$ and is parallel to $CI'$. Show that the lines $\ell_A$, $\ell_B$ and $\ell_C$ are concurrent.
