For a regular polygon, let r and R be the radii of the inscribed and the circumscribed cir…

Question

For a regular polygon, let $r$ and $R$ be the radii of the inscribed and the circumscribed circles. A $false$ statement  among the following is :

Accepted Answer

If $O$ is center of polygon and

$AB$ is one of the side, then by figure

$$\cos {\pi  \over n} = {r \over R}$$

$$ \Rightarrow {r \over R} = {1 \over 2},{1 \over {\sqrt 2 }},{{\sqrt 3 } \over 2}\,\,for$$

$n = 3,4,6$ respectively.

Solutions · 1