3. As shown in Figure 1, let the areas of the semicircles with diameters as the three sides of the right triangle $\triangle A B C$ be $S_{1}$, $S_{2}$, and $S_{3}$, and the area of the right triangle $\triangle A B C$ be $S$. Then the relationship between them is ( ).
(A) $S=S_{1}$
(B) $S_{1}=S_{2}+S_{3}$
(C) $S=S_{1}+S_{2}$
(D) $S=S_{1}+S_{2}+S_{3}$
3. B.
$$
\begin{array}{l}
S_{1}=\frac{\pi c^{2}}{2}, S_{2}=\frac{\pi a^{2}}{2}, S_{3}=\frac{\pi b^{2}}{2}, S=\frac{a b}{2}, \text { and } \\
c^{2}=a^{2}+b^{2} .
\end{array}
$$