Abstract
Two results are proved synthetically in Hilbert’s absolute geometry: (i) of all triangles inscribed in a circle, the equilateral one has the greatest area; (ii) of all triangles inscribed in a circle, the equilateral one has the greatest radius of the inscribed circle (which amounts, in the Euclidean case, to Euler’s inequality \(R\ge 2r\)).
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Pambuccian, V., Schacht, C. Euler’s inequality in absolute geometry. J. Geom. 109, 8 (2018). https://doi.org/10.1007/s00022-018-0414-6
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DOI: https://doi.org/10.1007/s00022-018-0414-6