In isosceles triangle $ABC$, sides $AB$ and $AC$ are congruent. Point…

Question

Prompt

In isosceles triangle

A B C

, sides

A B

and

A C

are congruent. Point

D

divides side

B C

such that the length of

\overline{B D}

\frac{4}{7}

of the length of

\overline{B C}

. Point

E

lies on side

A B

and point

F

lies on side

A C

such that when segments

D E

and

D F

are drawn, angle

B E D

is congruent to angle

C F D

. If the length of

\overline{B E}

8

, what is the length of

\overline{C F}