Problem
GEO-B2-M07-P008 Ratio on a Cevian
#8
★★★☆☆ Level 3 of 5
In triangle \(ABC\), point \(D\in BC\), \(P\in AD\). It is known that \([PBC]:[ABC]=3:8\). Find \(AP:PD\).
Compare the altitudes from \(P\) and \(A\) to base \(BC\).
Triangles \(PBC\) and \(ABC\) have common base \(BC\). Hence \(\frac{[PBC]}{[ABC]}=\frac{PD}{AD}=\frac{3}{8}\). Then \(AP=AD-PD\), so \(AP:PD=5:3\).
A first computation in the spirit of mass points.