Simple but tricky problem....

Geometry Level 2


The answer is 0.207.

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1 solution

Henry Pontzer
Apr 17, 2019

By drawing in multiple radii and utilizing the Pythagorean Theorem, we can see that the side length of the square is equal to ( 2 2 + 2 ) r (2\sqrt{2} + 2)r . Because the square has area 1, we know its side length is 1. If 1 = ( 2 2 + 2 ) r 1 = (2\sqrt{2} + 2)r , then r = 1 2 2 + 2 r = \frac{1}{2\sqrt{2} + 2} . Approximating 2 \sqrt{2} as 1.4, we can calculate r r as being 1 4.8 = 0.208 \frac{1}{4.8} = 0.208 . Plugging this into a calculator, instead, we get a more accurate answer of 0.207 \boxed{0.207} .

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