Circle perimeters

An inscribed circle is also described as an equilateral triangle with a side length of 8 cm. How many cm is the perimeter of the inscribed circle smaller than the circumference of the described circle?

Final Answer:

x =  14.5104 cm

Step-by-step explanation:

$$\begin{gathered} a=8\text{cm} \\ {r}_1=\sqrt{3}/6\cdot a=\sqrt{3}/6\cdot 8\doteq 2.3094\text{cm} \\ {r}_2=\sqrt{3}/3\cdot a=\sqrt{3}/3\cdot 8\doteq 4.6188\text{cm} \\ x=o_2-o_1 \\ x=2\pi \cdot r_2-2\pi \cdot r_1=2\cdot 3.1416\cdot 4.6188-2\cdot 3.1416\cdot 2.3094=14.5104\text{cm} \end{gathered}$$

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