Problem
GEO-B2-M07-P012 Finding Three Small Areas
#12
★★★☆☆ Level 3 of 5
In triangle \(ABC\), points \(D\in BC\), \(E\in CA\), \(BD:DC=2:3\), \(CE:EA=3:4\). Lines \(AD\) and \(BE\) meet at \(P\). Find \([PAB]:[PBC]:[PCA]\).
Let \([PAB]=x\), \([PBC]=y\), \([PCA]=z\).
From \(BD:DC=2:3\), we get \(x:z=2:3\). From \(CE:EA=3:4\), we get \(y:x=3:4\). Take \(x=8\). Then \(z=12\), \(y=6\). Hence \([PAB]:[PBC]:[PCA]=8:6:12=4:3:6\).
A standard technique for recovering areas.