20-18 In circle $O$, $Q$ is the midpoint of radius $O X$, and through $Q$ a line $A B \perp X Y$ is drawn. A semicircle is constructed with $A B$ as its diameter, intersecting $X Y$ at $M$. $A M$ and $B M$ intersect circle $O$ at $C$ and $D$, respectively. $A D$ is connected. If the radius of circle $O$ is $r$, then $A D$ is
(A) $\sqrt{2 r}$.
(B) $r$.
(C) a side of a non-regular polygon.
(D) $\frac{\sqrt{3}}{2} r$.
(E) $\sqrt{3} r$.
[Solution] Given $M A=M B$, and $\widehat{A M B}$ is a semicircle, $\therefore \angle A M B=90^{\circ}$, or $\angle M B A=45^{\circ}$. Connect $A O, O D$, then
$$
\begin{aligned}
& \angle A O D=2 \angle M B A=90^{\circ} . \\
\therefore \quad & A D=\sqrt{2} r .
\end{aligned}
$$

Therefore, the answer is $(A)$.