Problem
GEO-B1-M03-P017 A Parallel Through a Point on a Side
#17
★★★☆☆ Level 3 of 5
In triangle \(ABC\), point \(P\) lies on side \(AC\), with \(AP:PC=2:3\). Through \(P\), a line parallel to \(AB\) meets \(BC\) at \(E\). Find \(CE:EB\).
Compare triangles \(CPE\) and \(CAB\).
Since \(PE\parallel AB\), triangles \(CPE\) and \(CAB\) are similar. From \(AP:PC=2:3\), we get \(CP:CA=3:5\). Therefore \(CE:CB=3:5\). Since \(EB=CB-CE\), \(CE:EB=3:(5-3)=3:2\).
A good problem on choosing the correct large triangle: the similarity vertex here is \(C\).