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2015 OIM Problems/Problem 4

Revision as of 13:32, 14 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== 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 po...")
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Problem

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

\[\frac{FK}{KD}=\frac{EJ}{JD}\]

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

Solution

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See also

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