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Same angles on a trapezoidal base

Source: Sharygin Geometry Olympiad, Final Round 2016, Problem 6 grade 9

August 4, 2016
geometrytrapezoid

Problem Statement

The sidelines ABAB and CDCD of a trapezoid meet at point PP, and the diagonals of this trapezoid meet at point QQ. Point MM on the smallest base BCBC is such that AM=MDAM=MD. Prove that ∠PMB=∠QMB\angle PMB=\angle QMB.
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