Question 33
Let $ABC$ be a scalene triangle, $I$ its incenter and $k$ its circumcircle. Rays $BI, CI$ meet $k$ again at $S_b \neq B$, $S_c \neq C$, respectively. Prove that the tangent to $k$ at $A$, the line $S_bS_c$, and the line through $I$ parallel to $BC$ are concurrent. (Patrik Bak)