Abstract
Triangle Cevians play an important role in the study of Euclidean triangles. Accordingly, hyperbolic triangle Cevians, called gyrotriangle gyrocevians, play an important role in the study of hyperbolic triangles as well. The determination of the gyrocevian gyrolength and the measure of gyroangles that gyrocevians generate in gyrotriangles is presented. As an application, a special gyrocevian that generates special ingyrocircles is studied. Furthermore, gyrocevian concurrency conditions are uncovered and the hyperbolic version of the Theorem of Ceva is presented along with the related hyperbolic Brocard points.
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References
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Ungar, A.A. (2010). Gyrotriangle Gyrocevians. In: Hyperbolic Triangle Centers. Fundamental Theories of Physics, vol 166. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-8637-2_9
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DOI: https://doi.org/10.1007/978-90-481-8637-2_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-8636-5
Online ISBN: 978-90-481-8637-2
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