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circumcentet of (DEF) lies on (ABC)

Source: All-Russian MO 2009 Regional 9.7

August 27, 2024
geometryCircumcenterparallelogram

Problem Statement

Given a parallelogram ABCDABCD, in which the angle ∠ABC\angle ABC is obtuse. Line ADAD intersects the circle a second time ω\omega circumscribed around triangle ABCABC, at the point EE. Line CDCD intersects second time circle ω\omega at point FF. Prove that the circumcenter of triangle DEFDEF lies on the circle ω\omega.
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