Question 30
Let $ABC$ be an acute triangle and $I$ its incenter. Rays $BI$, $CI$ meet the circumcircle of triangle $ABC$ again at $S \neq B$, $T \neq C$, respectively. The segment $ST$ meets the sides $AB$, $AC$ at $K$, $L$, respectively. Prove that $AKIL$ is a rhombus. (Josef Tkadlec)