Let PQ be an h-line in a Poincare disc with center 0. a) The h-points A, B in PQ are located such that |PA| : |AB| :||BQ| = 1 : 1 : 2. The h-circle with h-center B and h-radius |AB|n intersects the radial line OBR at C,D with C closer to 0 than D, where R is the omega point along OB. If the e-distances |oc| = x ,\OB| = y ,\OD| = z, Prove that x = 2у-1 2-y b) In part a), if B is in the middle of the radial line, show that the h-circle passes through the center 0 of the Poincare circle.

Let PQ be an h-line in a Poincare disc with center 0. a) The h-points A, B in PQ are located such that |PA| : |AB| :||BQ| = 1 : 1 : 2. The h-circle with h-center B and h-radius |AB|n intersects the radial line OBR at C,D with C closer to 0 than D, where R is the omega point along OB. If the e-distances |oc| = x ,\OB| = y ,\OD| = z, Prove that x = 2у-1 2-y b) In part a), if B is in the middle of the radial line, show that the h-circle passes through the center 0 of the Poincare circle.

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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Question

Let PQ be an h-line in a Poincare disc with center 0.
a) The h-points A, B in PQ are located such that |PA| : |AB| : |BQ| = 1 : 1 : 2.
The h-circle with h-center B and h-radius |AB|n intersects the radial line OBR at C, D with
C closer to 0 than D, where R is the omega point along OB.
If the e-distances loc| = x ,\OB| = y ,\OD| = z, Prove that x =
%3D
2у-1
2-у
b) In part a), if B is in the middle of the radial line, show that the h-circle passes through the
center O of the Poincare circle.

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