IMO 2023 Shortlist G4
Let ABC be an acute-angled triangle with AB ă AC. Denote its circumcircle by Ω and denote the midpoint of arc CAB by S. ...
Category: Geometry
Problem
Let ABC be an acute-angled triangle with AB ă AC. Denote its circumcircle by Ω and denote the midpoint of arc CAB by S. Let the perpendicular from A to BC meet BS and Ω at D and E ‰ A respectively. Let the line through D parallel to BC meet line BE at L and denote the circumcircle of triangle BDL by ω. Let ω meet Ω again at P ‰ B. Prove that the line tangent to ω at P, and line BS intersect on the internal bisector of =BAC. (Portugal)