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trapezoid with bases equal to side and diagonal respectively

Source: 2009 Sharygin Geometry Olympiad Final Round problem 1 grade 8

July 26, 2018
geometrytrapezoidangle bisector

Problem Statement

Minor base BCBC of trapezoid ABCDABCD is equal to side ABAB, and diagonal ACAC is equal to base ADAD. The line passing through B and parallel to ACAC intersects line DCDC in point MM. Prove that AMAM is the bisector of angle ∠BAC\angle BAC.
A.Blinkov, Y.Blinkov
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