Classic Geometry Problem

Geometry Level 5

In the figure shown, ABCDABCD is an arbitrary rectangle. Point EE lies on side BCBC such that BEEC=2\frac{BE}{EC}=2 and point FF lies on CDCD such that CFFD=2\frac{CF}{FD}=2. Segments AEAE and ACAC intersect FBFB at points XX and YY, respectively. The ratio FY:YX:XBFY:YX:XB can be expressed as a:b:ca:b:c where aa, bb, and cc are coprime, positive integers. Find a+b+ca+b+c.

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