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points D,E, F,Q lie on the same circle.

Source: Indian Postal Coaching 2008 set 6 p1

May 25, 2020
geometryConcyclicparallelogramcyclic quadrilateral

Problem Statement

Let ABCDABCD be a quadrilateral that can be inscribed in a circle. Denote by PP the intersection point of lines ADAD and BCBC, and by QQ the intersection point of lines ABAB and DCDC. Let EE be the fourth vertex of the parallelogram ABCEABCE, and FF the intersection of lines CECE is PQPQ. Prove that the points D,E,FD,E, F, and QQ lie on the same circle.
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