2025 IMO Problems/Problem 2

Let $\Omega$ and $\Gamma$ be circles with centres $M$ and $N$ , respectively, such that the radius of $\Omega$ is less than the radius of $\Gamma$ . Suppose $\Omega$ and $\Gamma$ intersect at two distinct points $A$ and $B$ . Line $MN$ intersects $\Omega$ at $C$ and $\Gamma$ at $D$ , so that $C, M, N, D$ lie on $MN$ in that order. Let $P$ be the circumcentre of triangle $ACD$ . Line $AP$ meets $\Omega$ again at $E\neq A$ and meets $\Gamma$ again at $F\neq A$ . Let $H$ be the orthocentre of triangle $PMN$ .