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EM // AC wanted, isosceles trapezoid related

Source: 2020 Austrian Mathematical Olympiad Junior Regional Competition , Problem 3

December 18, 2020
geometrytrapezoid

Problem Statement

Given is an isosceles trapezoid ABCDABCD with AB∥CDAB \parallel CD and AB>CDAB> CD. The projection from DD on AB AB is EE. The midpoint of the diagonal BDBD is MM. Prove that EMEM is parallel to ACAC.
(Karl Czakler)
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