# Happy Accidents

Geometry Level 5

$$\triangle ABC$$ satisfies $$BC=8, AC=5, AB=7$$; let $$BE,CF$$ be its altitudes. $$X,Y$$ are on segments $$BC,EF$$ respectively such that $$CX=2, EY=\frac {6}{7}$$. Through $$Y$$ construct a line perpendicular to $$YX$$ to meet $$AC,AB$$ at $$M,N$$ respectively. Find $$\frac {YM}{YN}$$.

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