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- Feb 14, 2012

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Consider an acute triangle $ABC$ and let $P$ be an interior point of $ABC$. Suppose the lines $BP$ and $CP$, when produced, meet $AC$ and $AB$ in $E$ and $F$ respectively. Let $D$ be the point where $AP$ intersects the line segment $EF$ and $K$ be the foot of perpendicular from $D$ on to $BC$. Show that $DK$ bisects $\angle EKF$.

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