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O 5. An omega-triangle has vertices 0 = (0,0), = (1,0) and P = (0,h) where h > 0. (a) Prove that the hyperbolic segment PQ is an arc of a circle with equation (x-1)²+(y-k)² = k² for some k > 0. (b) Prove that the area of OPO is given by 2h A(h) = sin 1 1+h²

O 5. An omega-triangle has vertices 0 = (0,0), = (1,0) and P = (0,h) where h > 0. (a) Prove that the hyperbolic segment PQ is an arc of a circle with equation (x-1)²+(y-k)² = k² for some k > 0. (b) Prove that the area of OPO is given by 2h A(h) = sin 1 1+h²

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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O 5. An omega-triangle has vertices 0 = (0,0), = (1,0) and P = (0,h) where h > 0. (a) Prove that the hyperbolic segment PQ is an arc of a circle with equation (x-1)²+(y-k)² = k² for some k > 0. (b) Prove that the area of OPO is given by 2h A(h) = sin 1 1+h²
Transcribed Image Text:O 5. An omega-triangle has vertices 0 = (0,0), = (1,0) and P = (0,h) where h > 0. (a) Prove that the hyperbolic segment PQ is an arc of a circle with equation (x-1)²+(y-k)² = k² for some k > 0. (b) Prove that the area of OPO is given by 2h A(h) = sin 1 1+h²
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