$20 \cdot 82$ In a square $ABCD$ with side length 8, a circle is drawn through $A, D$ and is tangent to $BC$, then the radius of this circle is
(A) 4.
(B) $4 \sqrt{2}$.
(C) 5.
(D) $5 \sqrt{2}$.
(E) 6.
(13th American High School Mathematics Examination, 1962)
［Solution］As shown in the figure.
By the Pythagorean theorem, in Rt $\triangle A E O$ we have

$$
r^{2}=4^{2}+(8-r)^{2} \text {, }
$$

Therefore, the correct choice is $(C)$.