Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Euler's inequality

Revision as of 11:13, 4 June 2013 by Flamefoxx99 (talk | contribs) (→‎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

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=Euler%27s_inequality&oldid=52937"