Problem
GEO-B1-M07-P007 A Parallel and a Ratio
#7
★★☆☆☆ Level 2 of 5
In triangle \(ABC\), point \(D\) lies on \(BC\), with \(BD:DC=2:3\). Through \(D\), a line parallel to \(AB\) meets \(AC\) at point \(E\). Find \(CE:EA\).
Compare triangles \(CDE\) and \(CBA\).
Since \(DE\parallel AB\), triangles \(CDE\) and \(CBA\) are similar. We have \(CD:CB=3:5\), hence \(CE:CA=3:5\). Therefore \(CE:EA=3:2\).
Shows how a parallel line transfers a ratio from one side to another.