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trapezoid, angle bisectors and equidistant midpoint

Source: 2018 Oral Moscow Geometry Olympiad grades 8-9 p2

July 25, 2019
geometrytrapezoidangle bisectormidpoint

Problem Statement

Bisectors of angle CC and externalangle AA of trapezoid ABCDABCD with bases BCBC and ADAD intersect at point MM, and the bisector of angle BB and external angle DD intersect at point NN. Prove that the midpoint of the segment MNMN is equidistant from the lines ABAB and CDCD.
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