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calculations in a right trapezoid

Source: May Olympiad (Olimpiada de Mayo) 2001 L2

September 14, 2018
geometrytrapezoidright angle

Problem Statement

On the trapezoid ABCDABCD , side DADA is perpendicular to the bases ABAB and CDCD . The base ABAB measures 4545, the base CDCD measures 2020 and the BCBC side measures 6565. Let PP on the BCBC side such that BPBP measures 4545 and MM is the midpoint of DADA. Calculate the measure of the PMPM segment.
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