Question

A regular octagon of side 10 is inscribed in a circle. Find the radius of the circle.

Answer 1

$$\alpha=360\degree/8=45\degree$$

The Law of Cosines

$$10^2=r^2+r^2-2r^2\cos45\degree$$ $$r^2=\dfrac{100}{2-\sqrt{2}}$$ $$r=10\sqrt{1+\dfrac{\sqrt{2}}{2}}$$