Question

In triunghiul ABC , [AD] este mediana , D apartine (BC).Pe latura (AC) se considera punctul E. Daca AD intersectat cu BE = pct. F , aratati ca AF•EC=2AE•FD

Answer 1

$\displaystyle Se~aplica~\underline{teorema~lui~Menelaus}~in~triunghiul:~ \Delta ADC~cu \\ \\ transversala~ B-F-E:~ \frac{BC}{BD} \cdot \frac{FD}{FA} \cdot \frac{EA}{EC}=1 \Leftrightarrow \\ \\ \Leftrightarrow2 \cdot \frac{FD}{FA} \cdot \frac{EA}{EC} =1 \Rightarrow \boxed{AF \cdot EC=2AE \cdot FD}.$