Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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HYPERBOLIC AND SPHERICAL POWER OF A CIRCLE

  • Received : 2022.04.07
  • Accepted : 2022.06.21
  • Published : 2023.03.31
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Abstract

Suppose that a line passing through a given point P intersects a given circle 𝓒 at Q and R in the Euclidean plane. It is well known that |PQ||P R| 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.

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Acknowledgement

Heayong Shin was supported by NRF 2014R1A2A2A01007324, Sung-Eun Koh by NRF 2020R1A2C1A01003666 and Seong-Deog Yang by NRF 2012-042530.

References

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  2. G. Horv'ath, Hyperbolic plane geometry revisited, J. Geom. 106 (2015), no. 2, 341-362. https://doi.org/10.1007/s00022-014-0252-0
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