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What is the area of the shaded region in which the two semicircles are overlapping?

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A rectangle has a side length equal to 10.
Two semicircles are constructed with their diameters equal to the length of 10 and along opposite sides of the rectangle, as shown.
A circle is inscribed between the intersection points of the semicircles and tangent to the two sides of 10 on the rectangle.
What is the area of the shaded region in which the two semicircles are overlapping?

enter image description here

posted Mar 1, 2021 by Chahat Sharma

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