Difference between revisions of "Euler's inequality"

(Created page with "==Euler's Inequality== Euler's Inequality states that <cmath>R \gt 2r</cmath> ==Proof== Let the circumradius be <math>R</math> and inradius <math>r</math>. Let <math>d</math> be...")
 
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==Euler's Inequality==
 
==Euler's Inequality==
  
Euler's Inequality states that <cmath>R \gt 2r</cmath>
+
Euler's Inequality states that <cmath>R \ge 2r</cmath>
 +
 
 
==Proof==
 
==Proof==
 
Let the circumradius be <math>R</math> and inradius <math>r</math>. Let <math>d</math> be the distance between the circumcenter and the incenter. Then <cmath>d=\sqrt{R(R-2r)}</cmath>. From this formula, Euler's Inequality follows
 
Let the circumradius be <math>R</math> and inradius <math>r</math>. Let <math>d</math> be the distance between the circumcenter and the incenter. Then <cmath>d=\sqrt{R(R-2r)}</cmath>. From this formula, Euler's Inequality follows

Revision as of 11:13, 4 June 2013

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

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