AMC 12 2015b Problem 13

Quadrilateral $ABCD$ is inscribed in a circle with $\angle BAC=70^{\circ}, \angle ADB=40^{\circ}, AD=4,$ and $BC=6$. What is $AC$?

\textbf{(A)} 3+\sqrt{5} \textbf{(B)} 6 \textbf{(C)} \dfrac{9}{2}\sqrt{2} \textbf{(D)} 8-\sqrt{2} \textbf{(E)} 7