KöMaL 2016 B4802

The inscribed sphere of a right circular cone $\mathcal{K}$ is $\mathcal{G}$ . The centres of the spheres $g_1, g_2, \dots, g_n$ of radius $r$ form a regular $n$ -gon of side $2r$ . Furthermore, each sphere $g_i$ is tangent to both the lateral surface and the base of $\mathcal{K}$ , and also tangent to $\mathcal{G}$ . What may be the value of $n$ ?