Question 34
Consider an equilateral triangle $ABC$, where $AB=BC=CA=2011$. Let $P$ be a point inside $\triangle ABC$. Draw line segments passing through $P$ such that $DE\parallel BC$, $FG\parallel CA$ and $HI\parallel AB$. Suppose $DE:FG:HI=8:7:10$. Find $DE+FG+HI$.
