Difference between revisions of "Excenter"
| Line 3: | Line 3: | ||
==Properties of the Excenter== | ==Properties of the Excenter== | ||
*It lies on the angle bisector of the angle opposite to it in the triangle. | *It lies on the angle bisector of the angle opposite to it in the triangle. | ||
| − | *It is the point of concurrency of the angle bisector of the angle opposite to it in the triangle and the angle bisectors of the supplements of the angles which aren't opposite to it. These supplements | + | *It is the point of concurrency of the angle bisector of the angle opposite to it in the triangle and the angle bisectors of the supplements of the angles which aren't opposite to it. These supplements are the angles between the side opposite the angle opposite the excenter and the sides or the extensions of the sides adjacent to the angle opposite the excenter. |
*In any given triangle, <math>\frac{1}{r_1}+\frac{1}{r_2}+\frac{1}{r_3}=\frac{1}{r}</math>. <math>r_i</math> are the radii of the excircles, and <math>r</math> is the [[inradius]]. | *In any given triangle, <math>\frac{1}{r_1}+\frac{1}{r_2}+\frac{1}{r_3}=\frac{1}{r}</math>. <math>r_i</math> are the radii of the excircles, and <math>r</math> is the [[inradius]]. | ||
{{stub}} | {{stub}} | ||
Latest revision as of 11:53, 21 September 2024
An excenter, denoted 
, 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.
Properties of the Excenter
- It lies on the angle bisector of the angle opposite to it in the triangle.
- It is the point of concurrency of the angle bisector of the angle opposite to it in the triangle and the angle bisectors of the supplements of the angles which aren't opposite to it. These supplements are the angles between the side opposite the angle opposite the excenter and the sides or the extensions of the sides adjacent to the angle opposite the excenter.
- In any given triangle,
. 
are the radii of the excircles, and 
is the inradius.
. 
are the radii of the excircles, and 
is the This article is a stub. Help us out by expanding it.
