Question 10
Let $\triangle ABC$ be an acute triangle with $|AB|\lt|AC|$. Points $D$ and $E$ are given on the segments $AB$ and $AC$ respectively. Let $P$ be a point such that $|PB|=|PD|$ and $|PC|=|PE|$. Let $X$ be a point on the arc $AC$ of the circumcircle of $\triangle ABC$ not containing $B$. The line $XA$ intersects the circumcircle of $\triangle ADE$ again at $Y$. Prove that $|PX|=|PY|$.