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3

Part of 1997 Chile National Olympiad

Problems(1)

ABCD is a trapezoid, areas related (Chile 1997 P3)

Source:

5/27/2019
Let ABCD ABCD be a quadrilateral, whose diagonals intersect at O O . The triangles △AOB \triangle AOB , △BOC \triangle BOC , △COD \triangle COD have areas 1,2,41, 2, 4, respectively. Find the area of △AOD \triangle AOD and prove that ABCD ABCD is a trapezoid.
geometrytrapezoidareas