17. As shown in Figure 2, in trapezoid $A B C D$, $A B$ $/ / C D, B C=C D=$ $43, A D \perp B D, A C$ intersects $B D$ at point $O, P$ is the midpoint of $B D, O P=11$. If $A D=m \sqrt{n}(m, n \in$ $\mathbf{Z}_{+}, \sqrt{n}$ is in simplest radical form), then the value of $m+n$ is ( ).
(A) 65
(B) 132
(C) 157
(D) 194
(E) 215
17. D.

Since $A B / / C D$, we have $\angle A B D=\angle B D C$. From $B C=D C \Rightarrow \angle B D C=\angle D B C$. Combining $B C=C D, B P=P D$, we get $C P \perp B D$.
Thus, $\triangle A D B \backsim \triangle C P B$
$$
\begin{array}{l}
\Rightarrow 2=\frac{B D}{B P}=\frac{A B}{B C}=\frac{A B}{43} \\
\Rightarrow A B=86 .
\end{array}
$$

From $\triangle A B O \backsim \triangle C D O$
$$
\begin{array}{l}
\Rightarrow \frac{A B}{C D}=\frac{B O}{D O}=\frac{\frac{1}{2} B D+11}{\frac{1}{2} B D-11}=\frac{86}{43} \\
\Rightarrow B D=66 .
\end{array}
$$

Therefore, $A D=\sqrt{A B^{2}-B D^{2}}=4 \sqrt{190}$
$$
\begin{array}{l}
\Rightarrow m=4, n=190 \\
\Rightarrow m+n=194 .
\end{array}
$$