# Circles

Area of circle inscribed in a square is 14. What is the area of a circle circumscribed around a square?

Result

S =  28

#### Solution:

$S_1 = 14 = \pi r^2 \ \\ r = \sqrt{ S/\pi } \ \\ r_2^2 = r^2 + r^2 \ \\ r_2 = \sqrt{2} r = \sqrt{ 2S/\pi } \ \\ \ \\ S = \pi r_2^2 = \pi \cdot 2S / \pi = 2S = 28 \ \\$

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