If $R$ and $r$ be the radii of the circumcircle and incircle of a triangle, then how do I prove by synthetic geometry(i.e. without trigonometry) that $R\ge 2r$?
I am aware of a trigonometric proof but I am not quite sure if I can come up with a synthetic one. In case anyone is interested in the trigonometric proof, I can add it if you ask me to.