29. Let $A B C D$ be a rectangle with $A B=10$. Draw circles $C_{1}$ and $C_{2}$ with diameters $A B$ and $C D$ respectively. Let $P, Q$ be the intersection points of $C_{1}$ and $C_{2}$. If the circle with diameter $P Q$ is tangent to $A B$ and $C D$, then what is the area of the shaded region?
29. Ans: 25 .

Let $N$ be the midpoint of $C D$. Then $\angle P N Q=90^{\circ}$. So $P Q=5 \sqrt{2}$. Then the area of the shaded region is
$$
\begin{aligned}
A & =2\left[\frac{1}{2} \pi\left(\frac{P Q}{2}\right)^{2}+\frac{1}{2}(P N)^{2}-\frac{1}{4} \pi(P N)^{2}\right] \\
& =2\left[\frac{1}{2} \pi\left(\frac{5 \sqrt{2}}{2}\right)^{2}+\frac{1}{2} \cdot 5^{2}-\frac{1}{4} \pi \cdot 5^{2}\right]=25 .
\end{aligned}
$$