$ABC$ is a right-angled triangle. A square $ABDE$ is constructed on the opposite side of the hypotenuse $AB$  from $C$. The bisector of $\angle C$ cuts $DE$  at $F$ . If $BC=3AC$ and $\frac{DF}{EF}=\frac{a}{b}$, where $a$ and $b$ are two co-prime positive integers. Find $a+b$.