Given an acute triangle, inscribe the triangle of minimum perimeter.

Given the outside orange triangle ABC, your challenge is to move blue points X, Y, and Z so that one lies on each side of the triangle and the perimeter is as small as possible. For the initial triangle, with vertices at (0, 0), (5, 8), and (9, 1), the minimum perimeter is roughly 13.04. After you find that, you can move points A, B, and C and try another triangle if you like. You might even try a non-acute triangle. This wasn't part of Fagnano's Problem, but later, we'll briefly discuss it.

Click and drag blue dots X, Y, and Z to change the perimeter.

To return to Assignment 8 and the geometric approach, click here.