Folding a Quarter Circle

This problem comes from Bradley U's problem of the week page, http://hilltop.bradley.edu/~delgado/potw/potw.html, and it is problem number 142: http://hilltop.bradley.edu/~delgado/potw/s142.html. I found it in the April 16th, 2008 "Augarithms" newsletter, from Augsburg College (http://augsburg.edu/math).

A quarter of the unit circle is folded from the center to the edge, creasing at points D and F. The folded up portion forms a triangle.

Show that the maximum and the minimum areas of the triangle occur exactly where you'd expect them to, after a little thought. A good clue as to how to set up the problem can be found by examining the algebra window to see how I emulated the folded triangle. (But, notice that, for no good reason, I made the circle with radius = 4, and then had to "fudge" the text.)

Dave Matthews, Created with GeoGebra