. The correct answer is approximately equal to 18.7368.
For simplicity we rotate the image by 45 degrees. Then, using the relationship of the two circles, we define \((x,y)\) as the intersection of the small circle and one of the quarter circles and compute it. Using that, we determine the angles \(\alpha \simeq 0.9733\) and \(\beta \simeq 2.4188\) defined in the figure below:

We then compute the following quantities:

• The area of the green plus orange parts using \(\beta\) and the radius of the smaller circle (\(\simeq 14.0593\)).

• The area of the orange part using \(\alpha\) and the radius of the quarter circle (\(\simeq 4.6909\)).

Finally, by the latter quantity from the former one, we get the area of each of the green parts (\(\simeq 4.6909\)). Since we have 2 of these greens parts in the figure, we multiply the answer by 2 to obtain \(\simeq 18.7368\).

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