Abstract
Hyperbolic triangle excircles are called, in gyrolanguage, gyrotriangle exgyrocircles. These are determined in this chapter in terms of their gyrocenters and gyroradii. Their gyrocenters, in turn, are determined in terms of their gyrobarycentric coordinate representations with respect to the reference gyrotriangle. Moreover, relationships between the exgyroradii of a gyrotriangle exgyrocircles, and the gyrotriangle ingyroradius and circumgyroradius are obtained.
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References
Coxeter, H.S.M.: Introduction to Geometry, 2nd edn., p. 469. Wiley, New York (1969)
Coxeter, H.S.M., Greitzer, S.L.: Geometry Revisited. Math. Assoc. Am., New York (1967)
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Ungar, A.A. (2010). Gyrotriangle Exgyrocircles. In: Hyperbolic Triangle Centers. Fundamental Theories of Physics, vol 166. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-8637-2_8
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DOI: https://doi.org/10.1007/978-90-481-8637-2_8
Publisher Name: Springer, Dordrecht
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