https://artofproblemsolving.com/wiki/index.php?title=Excenter&feed=atom&action=history Excenter - Revision history 2020-10-20T12:05:11Z Revision history for this page on the wiki MediaWiki 1.31.1 https://artofproblemsolving.com/wiki/index.php?title=Excenter&diff=53074&oldid=prev Flamefoxx99: Created page with "An excenter, denoted $J_i$, is the center of an excircle of a triangle. An excircle is a circle tangent to the extensions of two sides and the third side. It is also ..." 2013-06-21T02:05:52Z <p>Created page with &quot;An excenter, denoted &lt;math&gt;J_i&lt;/math&gt;, is the center of an excircle of a triangle. An excircle is a circle tangent to the extensions of two sides and the third side. It is also ...&quot;</p> <p><b>New page</b></p><div>An excenter, denoted &lt;math&gt;J_i&lt;/math&gt;, is the center of an excircle of a triangle. An excircle is a circle tangent to the extensions of two sides and the third side. It is also known as an escribed circle.<br /> <br /> ==Properties of the Excenter==<br /> *It lies on the angle bisector of the angle opposite to it in the triangle.<br /> *In any given triangle, &lt;math&gt;\frac{1}{r_1}+\frac{1}{r_2}+\frac{1}{r_3}=\frac{1}{r}&lt;/math&gt;. &lt;math&gt;r_i&lt;/math&gt; are the radii of the excircles, and &lt;math&gt;r&lt;/math&gt; is the [[inradius]].<br /> <br /> {{stub}}</div> Flamefoxx99