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.