Geodesics of a Cone

Cone, Surface
Two points, A and B, are marked on the circumference of the base of a cone. Travelling along the surface of the cone, what is the shortest route from A to B? Click and drag to rotate the 3D view. Shift-click to pan. Scroll to zoom. Use the sliders to move B, change the dimensions of the cone, and unfold the cone into its net. Only click to see the solution once you have thought about it yourself! (Once you're done with that, click "allow winding" to see what happens.)