Collision detection.
Click "Closest Point" for an illustration of how the orange point is found. This method works for any parallelogram. Note that ClosestPoint[<point>, <polygon>] is pretty wild, and can't be used (Try it. Remember to drag the circle inside the rectangle, and play around. If it doesn't go crazy after a little while, leave a comment. For me, the results are [i]hilarious.[/i])