IMO Shortlist 2018 problem G7
Let be the circumcentre, and be the circumcircle of an acute-angled triangle . Let be an arbitrary point on , distinct from , , , and their antipodes in . Denote the circumcentres of the triangles , , and by , , and , respectively. The lines , , perpendicular to , , and pass through , , and , respectively. Prove that the circumcircle of triangle formed by , , and is tangent to the line .