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A problem about isosceles triangle and related circumcirles

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September 1, 2011
geometrycircumcircle

Problem Statement

Consider an isosceles triangle ABCABC with AB=ACAB=AC. Point DD is on the smaller arc ABAB of its circumcirle. Point EE lies on the continuation of segment ADAD beyond point DD so that both AA and EE lie in the same half-plane relative to BCBC. The circumcirle of triangle BDEBDE intersects side ABAB at point FF. Prove that lines EFEF and BCBC are parallel. (Author: R. Zhenodarov)
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