2018 IMO Shortlist G2

Let $A B C$ be a triangle with $A B=A C$, and let $M$ be the midpoint of $B C$. Let $P$ be a point such that $P B<P C$ and $P A$ is parallel to $B C$. Let $X$ and $Y$ be points on the lines $P B$ and $P C$, respectively, so that $B$ lies on the segment $P X, C$ lies on the segment $P Y$, and $\angle P X M=\angle P Y M$. Prove that the quadrilateral $A P X Y$ is cyclic. (Australia)

设$A B C$ 为三角形，$A B=A C$，$M$ 为$B C$ 的中点。令 $P$ 为一个点，使得 $P B<P C$ 且 $P A$ 与 $B C$ 平行。设$X$和$Y$分别为直线$P B$和$P C$上的点，使得$B$位于线段$P X上，C$位于线段$P Y$上，且$\angle P X M=\angle P Y M$。证明四边形$A P X Y$是循环的。 (澳大利亚)