# Classic Geometry Problem

Geometry Level 5

In the figure shown, $$ABCD$$ is an arbitrary rectangle. Point $$E$$ lies on side $$BC$$ such that $$\frac{BE}{EC}=2$$ and point $$F$$ lies on $$CD$$ such that $$\frac{CF}{FD}=2$$. Segments $$AE$$ and $$AC$$ intersect $$FB$$ at points $$X$$ and $$Y$$, respectively. The ratio $$FY:YX:XB$$ can be expressed as $$a:b:c$$ where $$a$$, $$b$$, and $$c$$ are coprime, positive integers. Find $$a+b+c$$.

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