Triunghi echilateral
Posted: Thu Mar 12, 2009 10:57 pm
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
\( \frac{a^3}{(r_a-r)^2}+\frac{b^3}{(r_b-r)^2}+\frac{c^3}{(r_c-r)^2}=\frac{2}{p}(r_a+r_b+r_c)^2 \)
atunci triunghiul ABC este echilateral.
Emil C. Popa, "Gh.Lazar'' 2007