Question 76
In $\triangle ABC$, let $D$, $E$, and $F$ be points on sides $BC$, $CA$, and $AB$, respectively, so that the segments $AD$, $BE$, and $CF$ are concurrent at point $P$. If $AF : FB = 4 : 5$ and the ratio of the area of $\triangle APB$ to that of $\triangle APC$ is $1 : 2$, determine $AE : AC$.