Question 143
Let $M$ be the midpoint of the base $\overline{BC}$ in the isosceles triangle $ABC$. Let $P$ be the point different from $A$ such that $PA \parallel BC$. Points $X$ and $Y$ lie on the rays $PB$ and $PC$, respectively, so that $B$ lies between $P$ and $X$, $C$ lies between $P$ and $Y$, and $\angle PXM = \angle PYM$ holds.
Prove that points $A, P, X$ and $Y$ are concyclic. (IMO Shortlist 2018)
Prove that points $A, P, X$ and $Y$ are concyclic. (IMO Shortlist 2018)