Euler's inequality
Revision as of 11:23, 4 June 2013 by Flamefoxx99 (talk | contribs)
Euler's Inequality states that
Proof
Let the circumradius be and inradius
. Let
be the distance between the circumcenter and the incenter. Then
From this formula, Euler's Inequality follows as
By the Trivial Inequality,
is positive. Since
has to be positive as it is the circumradius,
as desired