Problem 579: Quadrilateral, Diagonals, Triangles, Areas.
Level: Math Education, High School, SAT Prep, College

The figure shows a quadrilateral ABCD. The
diagonals AC and BD meet at O. If S_{1}, S_{2}, S_{3},
and S_{4}
are the areas of triangles AOB, BOC, COD, and AOD, respectively, prove
that S_{1}.S_{3} = S_{2}.S_{4} .