In $\triangle ABC,$ $AB=AC=25$ and $BC=23.$ Points $D,E,$ and $F$ are on sides $\overline{AB},$ $\overline{BC},$ and $\overline{AC},$ respectively, such that $\overline{DE}$ and $\overline{EF}$ are parallel to $\overline{AC}$ and $\overline{AB},$ respectively. What is the perimeter of parallelogram $ADEF$?
https://latex.artofproblemsolving.com/2/a/b/2aba6721a322cb3c799dbdf4c58c4551e0421ef0.png
+66 
