Other Excircle Properties
The distance d between the circumcenter and the center of an excircle is given by
where R is the circumradius and rex is the radius of the excircle.
The circular hull of the excircles is internally tangent to each of the excircles, and thus is an Apollonius circle. The radius of this Apollonius circle is where r is the incircle radius and s is the semiperimeter of the triangle.
The following relations hold among the inradius r, the circumradius R, the semiperimeter s, and the excircle radii r'a, rb, rc:
The circle through the centers of the three excircles has radius 2R.
If H is the orthocenter of triangle ABC, then
Read more about this topic: Incircle And Excircles Of A Triangle
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