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center of a rectangle lies in the segment connecting the projections

Source: May Olympiad (Olimpiada de Mayo) 2008 L2

September 11, 2018
geometryrectangleprojections

Problem Statement

Let ABCDABCD be a rectangle and PP be a point on the sideAD AD such that ∠BPC=90o\angle BPC = 90^o. The perpendicular from AA on BPBP cuts BPBP at MM and the perpendicular from DD on CPCP cuts CPCP in NN. Show that the center of the rectangle lies in the MNMN segment.
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