Puzzle of the Week #126 - Three Rectangles in a Circle

Fit three rectangles into a circle of radius 1.

What is the greatest combined area you can achieve?

3 rects in circle.JPG

(I usually like to have the solution be a whole number, but this is not possible in this case. It is however possible to express the solution in the form of √a + b, where a and b are whole numbers, but I’m also happy to accept an approximate answer to a couple of decimal places).