## Problem of the Day #251: Triangle Cutting
*November 25, 2011*

*Posted by Alex in : potd , trackback*

Instead of shopping (today is Black Friday!), Sreenath wants to go cut triangles. Points $A$, $B$, and $C$ are located at $(1, 1)$, $(5, 5)$, and $(3, 1)$ respectively. Sreenath chooses point $E$ on $\overline{AC}$ such that $BE$ cuts $\triangle ABC$ into two triangles with equal perimeters. Sreenath then chooses point $Q$ on $\overline{AC}$ such that $BQ$ cuts $\triangle ABC$ into two triangles with equal areas. Find $QE$.

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