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New characterisations of bicentric quadrilaterals

Published online by Cambridge University Press:  12 October 2022

Martin Josefsson
Martin Josefsson*
Affiliation:
Västergatan 25d, 285 37 Markaryd, Sweden e-mail: martin.markaryd@hotmail.com
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Extract

A bicentric quadrilateral is a convex quadrilateral that can have both an incircle (it is tangential) and a circumcircle (it is cyclic), see Figure 1. We know of only a dozen characterisations of bicentric quadrilaterals published before. In all of them the starting point is either a tangential or a cyclic quadrilateral, which then must satisfy some condition in order also to be of the other type. Before we proceed to prove seven new such necessary and sufficient conditions for bicentric quadrilaterals, we review one characterisation and one property of tangential quadrilaterals that we will apply later.

Type
Articles
Information
The Mathematical Gazette , Volume 106 , Issue 567 , November 2022 , pp. 414 - 426
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Copyright
© The Authors, 2022. Published by Cambridge University Press on behalf of The Mathematical Association

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