Find the area of the largest semicircle that can be inscribed in the unit square.

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## Thursday, March 4, 2010

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semicircle in a circle

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Find the area of the largest semicircle that can be inscribed in the unit square.

Posted in: Logical Puzzle,Mathematics Puzzle,Tricky Puzzle

## 1 Answers:

Consider a semicircle that is tangent to two sides of the square, with endpoints of its diameter on the other two sides. Express the length of the side of the square in terms of the radius of the semicircle.

The area of the largest semicircle that can be inscribed in the unit square is pi(3 − 2sqrt(2)) is approximately equal to 0.539.

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