Circumscribed decagon

In a regular decagon, the diameter of the circumscribed circle measures 10 cm. Determine the radius of the circle inscribed in this decagon.

Correct answer:

r =  9.5106 cm

Step-by-step explanation:

$$\begin{gathered} n=10 \\ R=10\text{cm} \\ \Phi =\frac{360}{2\cdot n}=\frac{360}{2\cdot 10}=18{}^{\circ } \\ \cos \Phi =r:R \\ r=R\cdot \cos \Phi =R\cdot \cos 18°=10\cdot \cos 18°=10\cdot 0.951057=9.511=9.5106\text{cm} \end{gathered}$$

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