Question 3
Let $ABC$ be a scalene triangle with circumcircle $\Omega$ and incenter $I$. Ray $AI$ meets segment $BC$ at $D$ and $\Omega$ again at $M$. The circle with diameter $DM$ meets $\Omega$ again at $K$. Lines $MK$ and $BC$ meet at $S$, and $N$ is the midpoint of $IS$. The circumcircles of $KID$ and $MAN$ intersect at $L_1,L_2$. Prove that $\Omega$ passes through the midpoint of either $IL_1$ or $IL_2$.
Proposed by Evan Chen. Source: Evan Chen’s third-party compilation, not an official publication. One editorial point; manual grading only.
Proposed by Evan Chen. Source: Evan Chen’s third-party compilation, not an official publication. One editorial point; manual grading only.