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Playing with trapezoids

Source: Indonesian Mathematical Olympiad 2014 Day 1 Problem 3

September 3, 2014
geometrytrapezoidparallelogramtrigonometrygeometric transformationdilationlogarithms

Problem Statement

Let ABCDABCD be a trapezoid (quadrilateral with one pair of parallel sides) such that AB<CDAB < CD. Suppose that ACAC and BDBD meet at EE and ADAD and BCBC meet at FF. Construct the parallelograms AEDKAEDK and BECLBECL. Prove that EFEF passes through the midpoint of the segment KLKL.
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