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 known as an escribed circle.

Properties of the Excenter

  • It lies on the angle bisector of the angle opposite to it in the triangle.
  • In any given triangle, $\frac{1}{r_1}+\frac{1}{r_2}+\frac{1}{r_3}=\frac{1}{r}$. $r_i$ are the radii of the excircles, and $r$ is the inradius.

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