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Show that circumcircle is tangent

Source: 67 Polish MO 2016 Second Round - Problem 2

April 30, 2018
geometrycircumcircletangentbisectorPoland

Problem Statement

In acute triangle ABCABC bisector of angle BACBAC intersects side BCBC in point DD. Bisector of line segment ADAD intersects circumcircle of triangle ABCABC in points EE and FF. Show that circumcircle of triangle DEFDEF is tangent to line BCBC.
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