Actually, I didn't read what you wrote properly. For some reason, I was assuming that A and B are **on** the circle when you had said clearly that they were exterior to the circle.

Captain Black's response is correct- Draw lines from A and B tangent to the circle. To do that, find the bisector of the line from A to the center of the circle, O, and construct a circle with that point as center and diameter |OA|. That circle will cut the original circle at two points. The line from A to either of those points is gives a tangent to the circle. Do the same with O and B. The straight line from A to the tangent point on the circle, the curve around the circle to the corresponding tangent point for B, then straight to B is the shortest route from A to B that does not go into the interior of the circle.