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
A
$\frac{5 \sqrt{2}}{2}$
B
$\frac{8 \sqrt{2}}{5}$
C
$\frac{5 \sqrt{2}}{3}$
D
$\frac{8 \sqrt{2}}{3}$
E
$\frac{9 \sqrt{2}}{4}$
F