$\text{A.}$ $65^{\circ}$ $\text{B.}$ $60^{\circ}$ $\text{C.}$ $50^{\circ}$ $\text{D.}$ $25^{\circ}$
【答案】 A

【解析】 【详解】解: $\because P A$ 与 $\odot O$ 相切于点 $A, A D$ 是 $\odot O$ 的直径,
\begin{aligned} & \therefore O A \perp P A, \\ & \therefore \angle P A O=90^{\circ}, \\ & \because \angle P=40^{\circ}, \\ & \therefore \angle A O P=50^{\circ}, \\ & \therefore \angle B O D=\angle A O P=50^{\circ}, \\ & \because O B=O D, \\ & \therefore \angle O B D=\angle O D B, \\ & \therefore \angle A D B=\frac{1}{2} \times\left(180^{\circ}-50^{\circ}\right)=65^{\circ}, \end{aligned}