Abstract
1. The idea is to look at what happen in a neighborhood of a vertex. Let ABC be a triangle that is not equilateral and suppose that AB < BC. Let a = BC − AB. Choose P inside ABC such that PB < a/4, PA − AB < a/4 and BC − PC < a/4. This is possible because of the continuity of the distance function.
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© 2000 Birkhäuser Boston
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Andreescu, T., Gelca, R. (2000). Geometry and Trigonometry. In: Mathematical Olympiad Challenges. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2138-8_4
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DOI: https://doi.org/10.1007/978-1-4612-2138-8_4
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4155-9
Online ISBN: 978-1-4612-2138-8
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