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Math·Geometry and Trigonometry·Lines, angles, and triangles

hard

In isosceles triangle $ABC$, sides $AB$ and $AC$ are congruent. Point $D$ divides side $BC$ such that the length of $BD$ is $\frac{2}{7}$ of the length of $BC$. 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 $BE$ is $14$, what is the length of $CF$?

A

28

B

35

C

49

D

98