Triunghi echilateral

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Marius Mainea
Gauss
Posts: 1077
Joined: Mon May 26, 2008 2:12 pm
Location: Gaesti (Dambovita)

Triunghi echilateral

Post by Marius Mainea »

Demonstrati ca daca are loc egalitatea:
\( \frac{a^3}{(r_a-r)^2}+\frac{b^3}{(r_b-r)^2}+\frac{c^3}{(r_c-r)^2}=\frac{2}{p}(r_a+r_b+r_c)^2 \)
atunci triunghiul ABC este echilateral.

Emil C. Popa, "Gh.Lazar'' 2007
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