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right trapezoid, double angle given, midpoint wanted

Source: Sharygin Geometry Olympiad 2015 Final 8.1

August 1, 2018
geometrytrapezoidmidpoint

Problem Statement

In trapezoid ABCDABCD angles AA and BB are right, AB=AD,CD=BC+AD,BC<ADAB = AD, CD = BC + AD, BC < AD. Prove that ∠ADC=2∠ABE\angle ADC = 2\angle ABE, where EE is the midpoint of segment ADAD.
(V. Yasinsky)
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