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a cos А + bcos В + с cos С <= р 1992 Kyiv City MO 10.4

Source:

July 20, 2021
inequalitiestrigonometrygeometric inequalitygeometry

Problem Statement

Prove theat for an arbitrary triangle holds the inequality acos⁡A+bcos⁡B+ccos⁡C≤p,a \cos A+ b \cos B + c \cos C \le p , where a,b,ca, b, c are the sides of the triangle, A,B,CA, B, C are the angles, pp is the semiperimeter.
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