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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