34. Consider an equilateral triangle $A B C$, where $A B=B C=C A=2011$. Let $P$ be a point inside $\triangle A B C$. Draw line segments passing through $P$ such that $D E\|B C, F G\| C A$ and $H I \| A B$. Suppose $D E: F G: H I=8: 7: 10$. Find $D E+F G+H I$.
34. Answer: 4022.
Set $D P=G P=a, I P=F P=b, E P=H P=c$. Then
$$
D E+F G+H I=(a+c)+(a+b)+(b+c)=2(a+b+c)=2 \times 2011=4022
$$