Problem

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 a. there is a regular polygon with

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

b. there is a regular polygon with

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

c. there is a regular polygon with

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

d. there is a regular polygon with

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