View source for 2015 OIM Problems/Problem 4

== Problem ==
In acute triangle <math>ABC</math>, point <math>D</math> is the foot of the perpendicular from <math>A</math> on side <math>BC</math>. Let <math>P</math> be a point on the segment <math>AD</math>. The lines <math>BP</math> and <math>CP</math> cut the sides <math>AC</math> and <math>AB</math> in <math>E</math> and <math>F</math> respectively. Let <math>J</math> and <math>K</math> be the feet of the perpendiculars from <math>E</math> and <math>F</math> on <math>AD</math> respectively. Show that

<cmath>\frac{FK}{KD}=\frac{EJ}{JD}</cmath>

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

== Solution ==
{{solution}}

== See also ==
[[OIM Problems and Solutions]]