MathDB

9.7

Part of 2009 All-Russian Olympiad Regional Round

Problems(1)

circumcentet of (DEF) lies on (ABC)

Source: All-Russian MO 2009 Regional 9.7

8/27/2024
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.
geometryCircumcenterparallelogram