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Bull. Korean Math. Soc. 2023; 60(2): 507-514
Online first article March 24, 2023 Printed March 31, 2023
https://doi.org/10.4134/BKMS.b220246
Copyright © The Korean Mathematical Society.
Hyperbolic and spherical power of a circle
Young Wook Kim, Sung-Eun Koh, Hyung Yong Lee, Heayong Shin, Seong-Deog Yang
Korea University; Konkuk University; Korea University; Chung-Ang University; Korea University
Suppose that a line passing through a given point $P$ intersects a given circle $\mathcal{C}$ at $Q$ and $R$ in the Euclidean plane. It is well known that $|PQ||PR|$ is independent of the choice of the line as long as the line meets the circle at two points. It is also known that similar properties hold in the 2-sphere and in the hyperbolic plane. New proofs for the similar properties in the 2-sphere and in the hyperbolic plane are given.
Keywords: Power of a circle, hyperbolic plane, sphere, conformal metric
MSC numbers: 53A35
Supported by: Heayong Shin was supported by NRF 2014R1A2A2A01007324, Sung-Eun Koh by NRF 2020R1A2C1A01003666 and Seong-Deog Yang by NRF 2012-042530.
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