What is the shortest path from $(-2,0)$ to $(2,0)$ that does not cross the unit circle?

Question

What could be the shortest path and distance to go from $A$ to $B$, provided that path should not cut the unit circle?

Tried by taking tangents of circle but could not get solution.

Answer 1

You go from $A$ to the circle at the point it is tangent, around the circle, and leave the circle when the tangent goes through $B$. To find the points of tangency, use the fact that for a circle the tangent is perpendicular to the radius at that point. A diagram is below. The line segments are tangent to the circle at $D,F$

Answer 2

In addition to @Ross Millikan's answer, note that the hypotenuse $AE$ is twice the leg $AF$, so $AFE$ is a 30-60-90 triangle.