Let ABC be a triangle with AB<AC and ω be its circumcircle. The tangent line to ω at A intersects line BC at D and let E be a point on ω such that BE is parallel to AD. DE intersects segment AB and ω at F and G, respectively. The circumcircle of BGF intersects BE at N. The line NF intersects lines AD and EA at S and T, respectively. Prove that DGST is cyclic. JBMO ShortlistgeometryAZE JBMO TST