Problem
GEO-B2-M07-P005 A Cevian and Area
#5
★★☆☆☆ Level 2 of 5
Point \(P\) lies inside triangle \(ABC\), and line \(AP\) meets \(BC\) at \(D\). Prove that \(\frac{BD}{DC}=\frac{[ABP]}{[ACP]}\).
Compare triangles with common base \(AP\).
Triangles \(ABP\) and \(ACP\) have common base \(AP\). Their altitudes from \(B\) and \(C\) to \(AP\) are in the ratio \(BD:DC\). Therefore \(\frac{[ABP]}{[ACP]}=\frac{BD}{DC}\).
The key formula for the whole module.