AHSME 1960 Problem 38

In this diagram $AB$ and $AC$ are the equal sides of an isosceles $\triangle ABC$, in which is inscribed equilateral $\triangle DEF$. Designate $\angle BFD$ by $a$, $\angle ADE$ by $b$, and $\angle FEC$ by $c$. Then:

$\textbf{(A)}\ b=\frac{a+c}{2} \textbf{(B)}\ b=\frac{a-c}{2} \textbf{(C)}\ a=\frac{b-c}{2} \textbf{(D)}\ a=\frac{b+c}{2} \textbf{(E)}\ \text{none of these}$