(p-a)(p-b)+(p-c)(p-a)>=sqrt3 S(IV All-Ukrainian Tourn.of Young Mathem. Final p2)

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(p-a)(p-b)+(p-c)(p-a)>=sqrt3 S(IV All-Ukrainian Tourn.of Young Mathem. Final p2)

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#1 h May 17, 2021, 7:01 PM

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Prove that in any triangle $(p-a) (p-b) + (p-c) (p-a)\ge \sqrt3 S$ , where $a, b, c$ are sides, $p$ is half perimeter, $S$ is area of a triangle.

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#2 h May 18, 2021, 3:06 AM

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parmenides51 wrote:

Prove that in any triangle $(p-a) (p-b) + (p-c) (p-a)\ge \sqrt3 S$ , where $a, b, c$ are sides, $p$ is half perimeter, $S$ is area of a triangle.

Hadwiger-Finsler inequality

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