Question 93
The incircle of $\triangle ABC$ with center $I$ touches the sides $AB$ and $AC$ at points $P$ and $Q$, respectively. $BI$ and $CI$ intersect $PQ$ at $K$ and $L$, respectively. Prove that circumcircle of $\triangle ILK$ touches the incircle of $\triangle ABC$ if and only if $AB + AC = 3BC$.