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TOT 2000 Spring OS1 sum of areas PAB, PCD = sum of areas PAD,PCB

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May 11, 2020
areasareageometrymidpoint

Problem Statement

The diagonals of a convex quadrilateral ABCDABCD meet at PP. The sum of the areas of triangles PABPAB and PCDPCD is equal to the sum of areas of triangles PADPAD and PCBPCB. Prove that PP is the midpoint of either ACAC or BDBD.
(Folklore)
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