Difference between revisions of "Exradius"
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<math>\frac{1}{r_1}+\frac{1}{r_2}+\frac{1}{r_3}=\frac{1}{r}</math> | <math>\frac{1}{r_1}+\frac{1}{r_2}+\frac{1}{r_3}=\frac{1}{r}</math> |
Revision as of 21:24, 1 August 2023
Excircle
The radius of an excircle. Let a triangle have exradius (sometimes denoted ), opposite side of length and angle , area , and semiperimeter . Then
(Johnson 1929, p. 189), where is the circumradius. Let be the inradius, then
and
(Casey 1888, p. 65) and
Some fascinating formulas due to Feuerbach are
Reference:
Weisstein, Eric W. "Exradius." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Exradius.html