Drag the point D.
Find the rectangle of maximum area inscribed in 
the region bounded by the x-axis and the parabola
given by y=-x²+1.  Can you find and prove the 
exact dimensions?

A = Point(xAxis)
B = Point(xAxis)
a = Line(A, B)
C = Point(a)
D = Point(a)
d = Circle(C, D)
E = Intersect(d, a, 2.0)
b = OrthogonalLine(E, a)
e = OrthogonalLine(D, a)
F = Intersect(c, b, 1.0)
f = Segment(E, F)
G = Intersect(c, e, 1.0)
g = Segment(F, G)
h = Segment(G, D)
i = Segment(D, E)
poly1, d_1, g_1, f_1, e_1 = Polygon(D, G, F, E)
Textpoly1: "Area " + (Name[D]) + (Name[G]) + (Name[F]) + (Name[E]) + " = " + poly1