2015 OIM Problems/Problem 4
Problem
In acute triangle 
, point 
is the foot of the perpendicular from 
on side 
. Let 
be a point on the segment 
. The lines 
and 
cut the sides 
and 
in 
and 
respectively. Let 
and 
be the feet of the perpendiculars from and on respectively. Show that
![\[\frac{FK}{KD}=\frac{EJ}{JD}\]](http://latex.artofproblemsolving.com/f/7/e/f7e21e465d965341157e2e9322e9a9a359648586.png)
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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