A circle of radius 1 is tangent to a circle of radius 2. The sides of $\triangle ABC$ are tangent to the circles as shown, and the sides $\overline{AB}$ and $\overline{AC}$ are congruent. What is the area of $\triangle ABC$? $\mathrm{(A)}\ \frac{35}{2}\qquad$ $\mathrm{(B)}\ 15\sqrt{2}\qquad$ $\mathrm{(C)}\ \frac{64}{3}\qquad$ $\mathrm{(D)}\ 16\sqrt{2}\qquad$ $\mathrm{(E)}\ 24$
A circle of radius $1$ is tangent to a circle of radius $3$. The sides of $\triangle ABC$ are tangent to the circles as shown, and the sides $\overline{AB}$ and $\overline{AC}$ are congruent. What is the area of $\triangle ABC$?
$\mathrm{(A)}\ \frac{35}{2}\qquad$ $\mathrm{(B)}\ 15\sqrt{2}\qquad$ $\mathrm{(C)}\ \frac{64}{3}\qquad$ $\mathrm{(D)}\ 16\sqrt{2}\qquad$ $\mathrm{(E)}\ 24$ 
