L'Hopital's original problem: Given two points outside a circle, find the point on a circle for which the sum of the two distances from the points to the circle is minimal.

Consider a suburban application of L'Hopital's problem. A city wants to place a new exit on the circular beltway around the city so that the sum of distances between the two suburbs (located outside the beltway) and the exit is minimal.

The NW suburb is located at (-2,3), and the NE suburb is at (4,4). The top half of the circular beltway y=√(4-x^2). Place the new beltway exit so that the sum of distances between the suburbs and the exit is minimal. You can physically experiment to get an approximation. Make a few guesses on the figure below. Now confirm your guesses by using calculus to solve the problem exactly.