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Tangent to Circumcirlce

Source: 2013 Baltic Way, Problem 12

December 31, 2013
geometrycircumcircletrapezoidgeometry unsolved

Problem Statement

A trapezoid ABCDABCD with bases ABAB and CDCD is such that the circumcircle of the triangle BCDBCD intersects the line ADAD in a point EE, distinct from AA and DD. Prove that the circumcircle oF the triangle ABEABE is tangent to the line BCBC.
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