如图所示，四边形 $A B C D$ 内接于圆, $\overline{A B}=5, \overline{A C}=3 \sqrt{5}, \overline{A D}=7$, $\angle B A C=\angle C A D$. 则圆的半径为
$\text{A.}$ $\frac{5 \sqrt{2}}{2}$
$\text{B.}$ $\frac{8 \sqrt{2}}{5}$
$\text{C.}$ $\frac{5 \sqrt{2}}{3}$
$\text{D.}$ $\frac{8 \sqrt{2}}{3}$
$\frac{9 \sqrt{2}}{4}$