Happy Accidents

Geometry Level 5

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


The answer is 1.0.

Xuming Liang by Xuming Liang , 23, USA

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