Draw in the tangents from A and B to the circle both on the same side of the diameter. Now the shortest path is along the tangent from A to the point of tangency, then along the circumference of the circle to the point of tangency of the other tangent, then along the tangent to B.
Depending on the exact wording of the question your job is to find the length of this path, or to prove that this is the shortest path.
For the latter you need to consider paths made up of two straight segments from the points to the circle and an arc connecting the points where the lines meet the circle. The fact that the length of an arc of a circle is greater than that of the corresponding chord may be useful.