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Problem with a trapezium-proving two lines are parallel

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July 17, 2012
geometrytrapezoid

Problem Statement

Let ABCDABCD be a trapezium with AB∥CDAB\parallel CD. Let PP be a point on ACAC such that CC is between AA and PP; and let X,YX, Y be the midpoints of AB,CDAB, CD respectively. Let PXPX intersect BCBC in NN and PYPY intersect ADAD in MM. Prove that MN∥ABMN\parallel AB.
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