Aria(AMPN)\geq \frac{mn}{3} Aria(ABC)

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Claudiu Mindrila
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Aria(AMPN)\geq \frac{mn}{3} Aria(ABC)

Post by Claudiu Mindrila »

Fie punctele \( M \) si \( N \) care apartin laturilor \( AC \) si \( AB \) respectiv, ale triunghiului \( ABC \), astfel incat \( MA=m \cdot MC \), \( NA=n\cdot NB \), unde \( m+n=2. \) Daca \( P \) este punctul de intersectie a dreptelor \( BM \) si \( CN \), sa se arate ca:
\( \text{aria}(AMPN)\geq \frac{mn}{3}\text{aria}(ABC) \).
Virgil Nicula, lista scurta, 2006
elev, clasa a X-a, C. N. "C-tin Carabella", Targoviste
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