Conc. interj. "Gheorghe Lazar" Sibiu 2010 probl. 4
Posted: Sun Mar 21, 2010 9:18 pm
Fie \( SABC \) o prisma triunghiulara oarecare si \( D, E, F \) puncte situate pe segmentele \( AB, BC, AC \) astfel ca:
\( \frac{AD}{DB}=\frac{1}{2}, \frac{BE}{EC}=\frac{1}{3}, \frac{CF}{FA}=\frac{1}{4} \).
Daca notam cu \( V_{SABC} \) volumul piramidei \( SABC \), aratati ca:
\( \frac{V_{SDEF}}{V_{SABC}}>\frac{2}{5} \).
Petrica Dicu, Sibiu
\( \frac{AD}{DB}=\frac{1}{2}, \frac{BE}{EC}=\frac{1}{3}, \frac{CF}{FA}=\frac{1}{4} \).
Daca notam cu \( V_{SABC} \) volumul piramidei \( SABC \), aratati ca:
\( \frac{V_{SDEF}}{V_{SABC}}>\frac{2}{5} \).
Petrica Dicu, Sibiu