# Many Points, Many Segments

Geometry Level 5

$$A,B,C$$ are points on circle $$\omega$$. Suppose points $$D,E$$ are on $$AB$$ and points $$F,G$$ are on $$AC$$ such that \begin{align} AD=24\\DE=4\\BE=12\\AF=15\\FG=27\\CG=18\end{align} If $$EG$$ interesect $$\omega$$ at $$X,Y$$, find $\frac {\sin \angle XDY}{\sin \angle XFY}$

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