Problem: In this diagram the center of the circle is O, the radius is a inches, chord EF is parallel to chord CD,O,G,H,J are collinear, and G is the midpoint of CD. Let K(sq. in.) represent the area of trapezoid CDFE and let R (sq. in.) represent the area of rectangle ELMF. Then as CD and EF are translated upward so that OG increases toward the value of a, while JH always equals HG, the ratio K:R becomes arbitrarily close to:
As OG increases toward the value a,x becomes arbitrarily close to zero, so that 2a−x​a−x​​ becomes arbitrarily close to 2a​a​​=21​​. Therefore, as OG increases toward the value a,RK​ becomes arbitrarily close to 21​​+21​=2​1​+21​
