Difference between revisions of "Euler's inequality"

Euler's Inequality

Euler's Inequality states that $$R \ge 2r$$

Proof

Let the circumradius be $R$ and inradius $r$. Let $d$ be the distance between the circumcenter and the incenter. Then $$d=\sqrt{R(R-2r)}$$. From this formula, Euler's Inequality follows