MEMO 2016 ekipno problem 5


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29. kolovoza 2018.
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Let ABC be an acute-angled triangle with |AB| \neq |AC|, and let O be its circumcentre. The line AO intersects the circumcircle \omega of ABC a second time in point D, and the line BC in point E. The circumcircle of CDE intersects the line CA a second time in point P. The line PE intersects the line AB in point Q. The line through O parallel to PE intersects the altitude of the triangle ABC that passes through A in point F.

Prove that |FP| = |FQ|.

Izvor: Srednjoeuropska matematička olimpijada 2016, ekipno natjecanje, problem 5