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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 S1, S2, S3, and S4 are the areas of triangles AOB, BOC, COD, and AOD, respectively, prove that S1.S3 = S2.S4 .
 

Quadrilateral with diagonals, Triangle, Area
 

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