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Geometry, SMO 2016, not easy

Source: Serbia National Olympiad 2016, day 1, P3

April 1, 2016
geometrycircumcircle

Problem Statement

Let ABCABC be a triangle and OO its circumcentre. A line tangent to the circumcircle of the triangle BOCBOC intersects sides ABAB at DD and ACAC at EE. Let A′A' be the image of AA under DEDE. Prove that the circumcircle of the triangle A′DEA'DE is tangent to the circumcircle of triangle ABCABC.
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