1. Prove that a circle in H projects to a Euclhdean circle in D. Conclude that not all triangles in hyperbolicgeometry have circumcircles (Hint: Draw a Euclidean circle that crosses the boundary of D and pick threepoints on it.)

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Prove that a circle in H projects to a Euclidean circle in D. Conclude that not all triangles in hyperbolic geometry have circumcireles (Hint: Draw a Euclidean circle that crosses the boundary of D and pick three points on it.)

Prove that a circle in H projects to a Euclidean circle in D. Conclude that not all triangles in hyperbolic geometry have circumcireles (Hint: Draw a Euclidean circle that crosses the boundary of D and pick three points on it.)

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter6: Circles

Section6.4: Some Constructions And Inequalities For The Circle

Problem 11E: X, Y, and Z are on circle O such that mXY=120, mYZ=130, and mXZ=110. Suppose that triangle XYZ is...

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Question

1. Prove that a circle in H projects to a Euclhdean circle in D. Conclude that not all triangles in hyperbolic
geometry have circumcircles (Hint: Draw a Euclidean circle that crosses the boundary of D and pick three
points on it.)

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