Norman Window: Modifiable Explorer

A [b]Norman window[/b] is a window that consists of a [b]rectangle mounted by a semicircle[/b]. [br]You can fix the perimeter of this Norman window using the input box at the bottom. [br][br]For any given fixed perimeter, how can we determine the dimensions of such a window that maximizes the [b][color=#bf9000]amount of sunlight[/color][/b] that can pass through it?
Drag the LARGE POINT (bottom left) along the xAxis to create various Norman windows with fixed perimeter. What do you notice?

Information: Norman Window: Modifiable Explorer