Square circles

Calculate the length of the described and inscribed circle to the square ABCD with a side of 5cm.

Correct result:

x =  15.708 cm
y =  22.2144 cm

Solution:

$$\begin{gathered} a=5\text{ cm } \\ {r}_1=a\mathrm{/}2=5\mathrm{/}2={\displaystyle \frac{5}{2}}=2\frac{1}{2}=2.5\text{ cm } \\ {r}_2=r_1\cdot \sqrt{2}=2.5\cdot \sqrt{2}\doteq 3.5355\text{ cm } \\ x=2\pi \cdot r_1=2\cdot 3.1416\cdot 2.5=15.708\text{ cm} \end{gathered}$$

$y=2\pi \cdot r_2=2\cdot 3.1416\cdot 3.5355=22.2144\text{ cm}$

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