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parallelogram if it has 2 // sides and PM/AP=1/4 - 1997 Romania NMO VII p4

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August 13, 2024
geometryparallelogram

Problem Statement

The quadrilateral ABCDABCD has two parallel sides. Let MM and NN be the midpoints of [DC][DC] and [BC][BC], and PP the common point of the lines AMAM and DNDN. If PMAP=14\frac{PM}{AP}=\frac{1}{4}, prove that ABCDABCD is a parallelogram.
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