Problem
GEO-B2-M06-P001 The Missing Ratio
#1
★★☆☆☆ Level 2 of 5
In triangle \(ABC\), points \(D,E,F\) lie on \(BC,CA,AB\). Given \(BD:DC=2:3\), \(CE:EA=3:4\). Find \(AF:FB\) if \(AD\), \(BE\), \(CF\) are concurrent.
Apply Ceva's theorem.
By Ceva, \(\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{AF}{FB}=1\). The first factors give \(\frac{1}{2}\), so \(\frac{AF}{FB}=2\). Answer: \(AF:FB=2:1\).
A basic substitution into Ceva.