For a regular polygon

MATHEMATICS · Single correct · GCSE · Mathematics · Geometry and Measures · Geometry and Measures

Problem

For a regular polygon, let

r

and

R

be the radii of the inscribed and circumscribed circles, respectively. A false statement among the following is (1) There is a regular polygon with

\frac{r}{R}=\frac{1}{2}

(2) There is a regular polygon with

\frac{r}{R}=\frac{1}{\sqrt{2}}

(3) There is a regular polygon with

\frac{r}{R}=\frac{2}{3}

(4) There is a regular polygon with

\frac{r}{R}=\frac{\sqrt{3}}{2}