答案：A
留意外心的坐標為 $\left(\dfrac{a}{2}, \dfrac{b}{2} \right)$。
把 $\left(\dfrac{a}{2}, \dfrac{b}{2} \right)$ 代入 $4x+16y=17a$，可得
$\begin{array}{rcl}
4 \left( \dfrac{a}{2} \right) +16\left(\dfrac{b}{2} \right) & = & 17a \\
2a +8b & = & 17a \\
8b & = & 15a \\
\dfrac{a}{b} & = & \dfrac{8}{15} \\
a:b & = & 8:15
\end{array}$
