Each side of square $A B C D$ is 8 . A circle is drawn through $A$ and $D$ so that it is tangent to $B C$. What is the radius of this circle?
(A) 4
(B) 5
(C) 6
(D) $4 \sqrt{2}$
(E) 5.25

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-150.jpg?height=342&width=349&top_left_y=409&top_left_x=1365)

Part C: Each question is worth 8 credits.