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Parallelogram and Circle

Source: All Russian Olympiad 2015 11.1

December 11, 2015
geometryparallelogram

Problem Statement

Parallelogram ABCDABCD is such that angle B<90B < 90 and AB<BCAB<BC. Points E and F are on the circumference of ω\omega inscribing triangle ABC, such that tangents to ω\omega in those points pass through D. If ∠EDA=∠FDC\angle EDA= \angle{FDC}, find ∠ABC\angle{ABC}.
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