Abstract
Some theorems from inversive and Euclidean circle geometry are extended to all affine Cayley-Klein planes. In particular, we obtain an analogue to the first step of Clifford’s chain of theorems, a statement related to Napoleon’s theorem, extensions of Wood’s theorem on similar-perspective triangles and of the known fact that the three radical axes of three given circles are parallel or have a point in common. For proving these statements, we use generalized complex numbers.
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Supported by a grant D01-761/24.10.06 from the Ministry of Education and Sciences, and by a grant 108/2007 from Sofia University.
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Martini, H., Spirova, M. Circle geometry in affine Cayley-Klein planes. Period Math Hung 57, 197–206 (2008). https://doi.org/10.1007/s10998-008-8197-5
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DOI: https://doi.org/10.1007/s10998-008-8197-5