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AB is tangent to the cicrumcircle of DEC'

Source: 2011 Oral Moscow Geometry Olympiad grades 10-11 p1

April 7, 2020
geometrycircumcircletangentsymmetry

Problem Statement

ADAD and BEBE are the altitudes of the triangle ABCABC. It turned out that the point C′C', symmetric to the vertex CC wrt to the midpoint of the segment DEDE, lies on the side ABAB. Prove that ABAB is tangent to the circle circumscribed around the triangle DEC′DEC'.
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