Length of one side for maximum area of trapezoid (solution by Calculus)

BC of trapezoid ABCD is tangent at any point on circular arc DE whose center is O. Find the length of BC so that the area of ABCD is maximum.

Trapezoid with one side tangent to the circle


As described by Alexander Bogomolny of cut-the-knot.org, for maximum area of trapezoid, the point of tangency should be at the midline of AB and DC, thus H is the midpoint of BC.