Concursul Nicolae Paun editia 2009 subiectul III

Moderators: Laurian Filip, Beniamin Bogosel, Filip Chindea

Post Reply
User avatar
Andi Brojbeanu
Bernoulli
Posts: 294
Joined: Sun Mar 22, 2009 6:31 pm
Location: Targoviste (Dambovita)

Concursul Nicolae Paun editia 2009 subiectul III

Post by Andi Brojbeanu »

Fie \( ABC \) un triunghi, \( D\in (BC), E\in (BC) \) astfel incat \( (AD \) este bisectoare, iar \( (AE \) mediana.
a) Aratati ca \( AD<\frac{2bc}{b+c} \), \( AE<\frac{b+c}{2} \), unde \( AB=c, AC=b \);
b) Daca \( b\neq c \) aratati ca exista \( F\in (DE) \) astfel incat \( AF<\sqrt{b}c \).

D.-S. Marinescu si V. Cornea, Hunedoara
Top
Post Reply

Return to “Clasa a IX-a”