IMO Shortlist 2018 problem G4


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3. listopada 2019.
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A point T is chosen inside a triangle ABC. Let A_1, B_1, and C_1 be the reflections of T in BC, CA, and AB, respectively. Let \Omega be the circumcircle of the triangle A_1B_1C_1. The lines A_1T, B_1T, and C_1T meet \Omega again at A_2, B_2, and C_2, respectively. Prove that the lines AA_2, BB_2, and CC_2 are concurrent on \Omega.

Izvor: https://www.imo-official.org/problems/IMO2018SL.pdf