IMO Shortlist 2018 problem G7


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3. listopada 2019.
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Let O be the circumcentre, and \Omega be the circumcircle of an acute-angled triangle ABC. Let P be an arbitrary point on \Omega, distinct from A, B, C, and their antipodes in \Omega. Denote the circumcentres of the triangles AOP, BOP, and COP by O_A, O_B, and O_C, respectively. The lines \ell_A, \ell_B, \ell_C perpendicular to BC, CA, and AB pass through O_A, O_B, and O_C, respectively. Prove that the circumcircle of triangle formed by \ell_A, \ell_B, and \ell_C is tangent to the line OP.

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