Problem 416: Triangle, Cevians, Trisectors, Area

Online Geometry

The figure shows a triangle ABC of area S with the cevians AA', BB', and CC' so that AB' = AC/3, BC' = AB/3, and CA' = BC/3. Prove that (1) Areas of triangles ABB', BCC', and CAA' are equal to S/3, (2) Areas of triangles ABD, BCE, and CAF are equal to 2S/7, (3) Area triangle DEF = S/7.
 

Triangle area, cevian, trisector
 

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