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trapezoid and areas wanted - 1993 Cono Sur Shortlist G2

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October 23, 2021
geometrytrapezoid

Problem Statement

Let ABCDABCD be a quadrilateral and let OO be the point of intersection of diagonals ACAC and BDBD. Knowing that the area of triangle AOBAOB is equal to 1 1, the area of triangle BOCBOC is equal to 22, and the area of triangle CODCOD is equal to 44, calculate the area of triangle AODAOD and prove that ABCDABCD is a trapezoid.
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