Abstract
In this note we prove the following result: for every \(\alpha \in (0,\pi )\) and for a given convex body K in the plane, with minimal width w, there exists a chord [x, y] with length larger than or equal to \(w\cos \frac{\alpha }{2}\) such that there are support lines of K through x and y which form an angle \(\alpha .\) Moreover, if there is no such chord with length exceeding \(w\cos \frac{\alpha }{2}\), then K is a Euclidean disc.
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We thank the unknown referee for many valuable suggestions which improve the exposition of the paper.
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Jerónimo-Castro, J., Yee-Romero, C. An inequality for the length of isoptic chords of convex bodies. Aequat. Math. 93, 619–628 (2019). https://doi.org/10.1007/s00010-018-0611-2
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DOI: https://doi.org/10.1007/s00010-018-0611-2