Exradius
Excircle
The radius of an excircle. Let a triangle have exradius r_A (sometimes denoted rho_A), opposite side of length a and angle A, area Delta, and semiperimeter s. Then
(Johnson 1929, p. 189), where R is the circumradius. Let r be the inradius, then
| 4R=r_1+r_2+r_3-r |
(4)
|
(Casey 1888, p. 65) and
| rr_1r_2r_3=Delta^2. |
(6)
|
Some fascinating formulas due to Feuerbach are
(Johnson 1929, pp. 190-191).
See also
Circle, Circumradius, Excircles, Inradius, RadiusExplore with Wolfram|Alpha
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References
Casey, J. A Sequel to the First Six Books of the Elements of Euclid, Containing an Easy Introduction to Modern Geometry with Numerous Examples, 5th ed., rev. enl. Dublin: Hodges, Figgis, & Co., 1888.Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, 1929.Mackay, J. S. "Formulas Connected with the Radii of the Incircle and Excircles of a Triangle." Proc. Edinburgh Math. Soc. 12, 86-105.Mackay, J. S. "Formulas Connected with the Radii of the Incircle and Excircles of a Triangle." Proc. Edinburgh Math. Soc. 13, 103-104.Referenced on Wolfram|Alpha
ExradiusCite this as:
Weisstein, Eric W. "Exradius." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Exradius.html