What name shall I give to this problem? - 2

Geometry Level 5

In $\triangle ABC$ , $D$ and $E$ are points on $BC$ such that $BD = DE = EC$ . $F$ is a point on $AC$ such that $AF=FC$ . If $AD$ and $AE$ intersect $BF$ respectively at $P$ and $Q$ . Then, the ratio $\dfrac{BP}{PQ}$ can be expressed as $\dfrac{a}{b}$ , where $a$ and $b$ are coprime integers. Find $10a+b$ .