# Difference between revisions of "2013 USAJMO Problems/Problem 5"

Quadrilateral $XABY$ is inscribed in the semicircle $\omega$ with diameter $XY$. Segments $AY$ and $BX$ meet at $P$. Point $Z$ is the foot of the perpendicular from $P$ to line $XY$. Point $C$ lies on $\omega$ such that line $XC$ is perpendicular to line $AZ$. Let $Q$ be the intersection of segments $AY$ and $XC$. Prove that $$\dfrac{BY}{XP}+\dfrac{CY}{XQ}=\dfrac{AY}{AX}$$.