Math Problem

A rectangle and an isosceles triangle are inscribed in a circle with a radius of 1. The rectangle has height, h, and base, b. For what value of h are the areas of the rectangle and triangle the same?

The heights of the triangles (for there are two: http://i34.tinypic.com/2rcsprd.png) are {h \over 2}+r and r - {h \over 2}, where r is the radius of the circle.
b is fixed based on h, according to the formula b = sqrt{-{h^2 \over 4} + r^2}*2 (this follows from the formula for the circle).

The formula for the surface of the rectangle is sqrt{-{h^2 \over 4} + r^2}*2*h, and for the triangles {({{h \over 2}+r}) * sqrt{-{h^2 \over 4} + r^2}*2} \over 2 and {(r - {h \over 2}) * sqrt{-{h^2 \over 4} + r^2}*2} \over 2.
The problem therefore reduces to finding the values of h for sqrt{-{h^2 \over 4} + r^2}*2*h = {{({{h \over 2}+r}) * sqrt{-{h^2 \over 4} + r^2}*2} \over 2} on the one hand, and sqrt{-{h^2 \over 4} + r^2}*2*h = {{(r - {h \over 2}) * sqrt{-{h^2 \over 4} + r^2}*2} \over 2} on the other.
(Hint: they will be the same.)

Since this is your homework, I suggest you solve those.