SAT Lines, angles, and triangles Question

In isosceles triangle $ABC$, sides $AB$ and $AC$ are congruent. Point $D$ divides side $BC$ such that the length of $\overline{BD}$ is $\frac{2}{7}$ of the length of $\overline{BC}$. Point $E$ lies on side $AB$ and point $F$ lies on side $AC$ such that when segments $DE$ and $DF$ are drawn, angle $BED$ is congruent to angle $CFD$. If the length of $\overline{BE}$ is 14, what is the length of $\overline{CF}$?