Inegalitate intr-un triunghi

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alex2008
Leibniz
Posts: 464
Joined: Sun Oct 19, 2008 3:23 pm
Location: Tulcea

Inegalitate intr-un triunghi

Post by alex2008 »

Daca \( a,b,c \) sunt lungimile laturilor triunghiului \( ABC \) , iar \( A,B,C \) sunt masurile in radiani ale unghiurilor triunghiului , sa se arate ca :

\( \frac{aA+bB+cC}{a+b+c}\ge \frac{\pi}{3} \)
. A snake that slithers on the ground can only dream of flying through the air.
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Marius Mainea
Gauss
Posts: 1077
Joined: Mon May 26, 2008 2:12 pm
Location: Gaesti (Dambovita)

Post by Marius Mainea »

Evident tripletele \( (a,b,c) \) si \( (A,B,C) \) sunt la fel orientate si aplicam inegalitatea Cebasev tinand cont ca \( A+B+C=\pi \)
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