Answer
$18.7\ cm$
Work Step by Step
1. We know that the two wheels should travel the same arc length.
2. For the smaller wheel, we have the arc length traveled as $L_1=11.7\times80^\circ\times\frac{\pi}{180^\circ}\ cm$
3. For the larger wheel, we have the arc length traveled as $L_2=r\times 50^\circ\times\frac{\pi}{180^\circ}\ cm$
4. Let $L_2=L1$, we can find $r=\frac{11.7\times80}{50}\approx18.7\ cm$
