3. As shown in Figure 1, a symmetrical shape is formed by 3 squares with side lengths of 1. The minimum radius of a circle that can completely cover this shape is ( ).
(A) $\sqrt{2}$
(B) $\frac{\sqrt{5}}{2}$
(C) $\frac{5}{4}$
(D) $\frac{5 \sqrt{17}}{16}$
3. (D).

As shown in Figure 3, we have
$$
\left\{\begin{array}{l}
a^{2}+1=r^{2}, \\
(2-a)^{2}+\left(\frac{1}{2}\right)^{2}=r^{2}
\end{array}\right.
$$

Solving, we get $a=\frac{13}{16}, r=\frac{5 \sqrt{17}}{16}$.