Question 185
You are given two diameters $AB$ and $CD$ of circle $\Omega$ with radius $1$. A circle is drawn in one of the smaller sectors formed such that it is tangent to $AB$ at $E$, tangent to $CD$ at $F$, and tangent to $\Omega$ at $P$. Lines $PE$ and $PF$ intersect $\Omega$ again at $X$ and $Y$. What is the length of $XY$, given that $AC=\frac{2}{3}$?