IMO Shortlist 2007 problem G5

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Dodao/la: arhiva
2. travnja 2012.
Let ABC be a fixed triangle, and let A_1, B_1, C_1 be the midpoints of sides BC, CA, AB, respectively. Let P be a variable point on the circumcircle. Let lines PA_1, PB_1, PC_1 meet the circumcircle again at A', B', C', respectively. Assume that the points A, B, C, A', B', C' are distinct, and lines AA', BB', CC' form a triangle. Prove that the area of this triangle does not depend on P.

Author: Christopher Bradley, United Kingdom
Izvor: Međunarodna matematička olimpijada, shortlist 2007