Question

A regular octagon is inscribed in a circle of radius 1. Find a side of the octagon.

Answer 1

• The radius of circle is $1$
• The angle between adjacent sides of regular octagon is $(8-2)180/8=135$
• The angle made by each side at center is $360/8=45$
• Let the side length of regular octagon be $a$
• By sine rule , we get $a/sin45=1/sin\left(62.5\right)$ , which implies $a=sin45/sin\left(62.5\right)=\sqrt{2-\sqrt{2}}$