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quadrilateral PEFG is maximum

Source: China TST 1988, problem 6

June 27, 2005
geometrytrapezoidgeometry unsolved

Problem Statement

Let ABCDABCD be a trapezium AB//CD,AB // CD, MM and NN are fixed points on AB,AB, PP is a variable point on CDCD. E=DN∩APE = DN \cap AP, F=DN∩MCF = DN \cap MC, G=MC∩PBG = MC \cap PB, DP=λ⋅CDDP = \lambda \cdot CD. Find the value of λ\lambda for which the area of quadrilateral PEFGPEFG is maximum.
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