IMO 2024 Shortlist G6
Let ABC be an acute triangle with AB ă AC, and let Γ be the circumcircle of ABC. Points X and Y lie on Γ so that XY and ...
Category: Geometry
Problem
Let ABC be an acute triangle with AB ă AC, and let Γ be the circumcircle of ABC. Points X and Y lie on Γ so that XY and BC intersect on the external angle bisector of =BAC. Suppose that the tangents to Γ at X and Y intersect at a point T on the same side of BC as A, and that TX and TY intersect BC at U and V , respectively. Let J be the centre of the excircle of triangle TUV opposite the vertex T. Prove that AJ bisects =BAC. (Poland) 8 Bath, United Kingdom, 10th –22nd July 2024