Question

内切圆的半径是根号3,外接圆的半径2的正多边形的边数是

Answer 1

设边数是n,内切圆的半径是r,外接圆的半径是R,

则

cos[(2π)/(2n)]=r/R,

cos(π/n)=√3/2,

cos(π/6)=√3/2,

n=6