Square circles

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

Result

x =  15.708 cm
y =  22.214 cm

Solution:

a=5 cm r1=a/2=5/2=52=2.5 cm r2=r1 2=2.5 23.5355 cm x=2π r1=2 3.1416 2.515.70815.708 cma=5 \ \text{cm} \ \\ r_{1}=a/2=5/2=\dfrac{ 5 }{ 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 \doteq 15.708 \doteq 15.708 \ \text{cm}
y=2π r2=2 3.1416 3.535522.214422.214 cmy=2 \pi \cdot \ r_{2}=2 \cdot \ 3.1416 \cdot \ 3.5355 \doteq 22.2144 \doteq 22.214 \ \text{cm}



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