Consider an acute-angled triangle ABC with AB<AC and let ω be its circumscribed circle. Let tB and tC be the tangents to the circle ω at points B and C, respectively, and let L be their intersection. The straight line passing through the point B and parallel to AC intersects tC in point D. The straight line passing through the point C and parallel to AB intersects tB in point E. The circumcircle of the triangle BDC intersects AC in T, where T is located between A and C. The circumcircle of the triangle BEC intersects the line AB (or its extension) in S, where B is located between S and A. Prove that ST, AL, and BC are concurrent.Vangelis Psychas and Silouanos Brazitikos geometrybarycentric coordinatesBalkansymmedianBalkan Mathematics Olympiad