Problem
GEO-B2-M07-P013 Area Fraction and Cevian Division
#13
★★★☆☆ Level 3 of 5
In triangle \(ABC\), point \(D\in BC\), \(P\in AD\). If \(AP:PD=4:3\), find \([PBC]:[ABC]\).
Area \(PBC\) is to \(ABC\) as the distance from \(P\) to \(BC\) is to the distance from \(A\) to \(BC\).
Since \(AP:PD=4:3\), we have \(PD:AD=3:7\). Triangles \(PBC\) and \(ABC\) have common base \(BC\), so \([PBC]:[ABC]=PD:AD=3:7\).
An important formula for points on a cevian.