AMC 10 2015a Problem 19

The isosceles right triangle $ABC$ has right angle at $C$ and area $12.5$. The rays trisecting $\angle ACB$ intersect $AB$ at $D$ and $E$. What is the area of $\bigtriangleup CDE$? $\textbf{(A) }\dfrac{5\sqrt{2}}{3} \textbf{(B) }\dfrac{50\sqrt{3}-75}{4} \textbf{(C) }\dfrac{15\sqrt{3}}{8} \textbf{(D) }\dfrac{50-25\sqrt{3}}{2} \textbf{(E) }\dfrac{25}{6}$