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International Olympiad of metropolises 2016 P4

Source: International Olympiad of metropolises 2016

September 7, 2016
IOMgeometry

Problem Statement

A convex quadrilateral ABCDABCD has right angles at AA and CC. A point EE lies on the extension of the side ADAD beyond DD so that∠ABE=∠ADC\angle ABE =\angle ADC. The point KK is symmetric to the point CC with respect to point AA. Prove that∠ADB=∠AKE\angle ADB =\angle AKE .
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