Abstract
In this paper the following is proved: Let K ⊂ \( \mathbb{E}^2 \) be a smooth strictly convex body, and let L ⊂ \( \mathbb{E}^2 \) be a line. Assume that for every point x ∈ L/K the two tangent segments from x to K have the same length, and the line joining the two contact points passes through a fixed point in the plane. Then K is an Euclidean disc.
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Communicated by Imre Bárány
Supported by CONACYT, SNI 38848
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Jerónimo-Castro, J., Roldán-Pensado, E. A characteristic property of the Euclidean disc. Period Math Hung 59, 213–222 (2009). https://doi.org/10.1007/s10998-009-0213-9
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DOI: https://doi.org/10.1007/s10998-009-0213-9