Question 5
Quadrilateral $XABY$ is inscribed in a semicircle with diameter $XY$. Segments $AY$ and $BX$ meet at $P$. Let $Z$ be the perpendicular projection of $P$ onto line $XY$. Point $C$ lies on the semicircle with $XC\perp AZ$, and $Q=AY\cap XC$. Prove
$$\frac{BY}{XP}+\frac{CY}{XQ}=\frac{AY}{AX}.$$
Proposed by Zuming Feng (credited in the supplied notes).
$$\frac{BY}{XP}+\frac{CY}{XQ}=\frac{AY}{AX}.$$
Proposed by Zuming Feng (credited in the supplied notes).