22. Let $O$ be an interior point of $\triangle A B C$. Extend $A O$ to meet the side $B C$ at $D$. Similarly, extend $B O$ and $C O$ to meet $C A$ and $A B$ respectively at $E$ and $F$. If $A O=30, F O=20, B O=60, D O=10$ and $C O=20$, find $E O$.
22. Ans: 20
We have
$$
\frac{O D}{A D}=\frac{[B O C]}{[A B C]}, \quad \frac{O E}{B E}=\frac{[A O C]}{[A B C]}, \quad \frac{O F}{C F}=\frac{[A O B]}{[A B C]}
$$

Thus
$$
\frac{O D}{A D}+\frac{O E}{B E}+\frac{O F}{C F}=1 \quad \Rightarrow \quad O E=20 .
$$