SMO 2007 Open Round 1 Question 22

Let $O$ be an interior point of triangle $ABC$. Extend $AO$ to meet $BC$ at $D$; similarly extend $BO,CO$ to meet $CA,AB$ at $E,F$, respectively. If $AO=30$, $FO=20$, $BO=60$, $DO=10$, $CO=20$, find $EO$.