Problem
GEO-B2-M06-P004 The Missing Menelaus Ratio
#4
★★☆☆☆ Level 2 of 5
In triangle \(ABC\), points \(D\in BC\), \(E\in CA\), and \(F\) lies on the extension of \(AB\) beyond \(B\). Points \(D,E,F\) are collinear, \(BD:DC=2:5\), \(CE:EA=5:3\). Find \(AF:FB\).
Use the positive form of Menelaus with one external point.
By Menelaus, \(\frac{2}{5}\cdot\frac{5}{3}\cdot\frac{AF}{FB}=1\). We get \(\frac{2}{3}\cdot\frac{AF}{FB}=1\), hence \(AF:FB=3:2\).
A basic Menelaus computation.