A common external tangent to circles ω1 and ω2 touches them at points T1,T2 respectively. Let A be an arbitrary point on the extension of T1T2 beyond T1, and B be a point on the extension of T1T2 beyond T2 such that AT1=BT2. The tangents from A to ω1 and from B to ω2 distinct from T1T2 meet at point C. Prove that all nagelians of triangles ABC from C have a common point. geometrynagelianconcurrencytangent circlesSharygin Geometry OlympiadSharygin 2023