More on Comparing Areas

Let the side lengths of the right triangle be $a$ , $b$ , and $c$ , where $c$ is the hypotenuse and the blue area be $B$ . Then the blue area is given by:

$\begin{aligned} B & = \frac {\pi c^2}4 - R \\ \implies R & = \frac {\pi c^2}4 - B \end{aligned}$

and the green area:

$\begin{aligned} G & = \frac {\pi a^2}4 + \frac {\pi a^2}4 - B & \small \blue{\text{Since }a^2+b^2=c^2} \\ & = \frac {\pi c^2}4 - B \end{aligned}$

Therefore, $\boxed{G=R}$ .