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Geometry Level 3

There are 2 circles and a square. The square is inscribed in the larger circle, and the smaller circle is inscribed in the square.

The sum of the area of the larger circle not being enclosed in the square and the area of the square not being enclosed in the smaller circle is equal to the area of the ......

The square The smaller circle None of them The larger circle

Winston Choo by Winston Choo , 46, Singapore

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1 solution

Jeremy Galvagni
Nov 11, 2018

Let the radius of the small circle be O C = r OC=r , then the radius of the larger circle O A = r 2 OA=r\sqrt{2} .

The region described is the green and blue together, it is an annulus. The area of this annulus is π ⋅ ( r 2 ) 2 − π ⋅ r 2 = π ⋅ r 2 \pi\cdot (r\sqrt{2})^{2} - \pi\cdot r^{2} = \pi\cdot r^{2}

Which is precisely the area of The smaller circle \boxed{\text{The smaller circle}}

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