IMO 2006 Shortlist G6
Circles ω1 and ω2 with centres O1 and O2 are externally tangent at point D and internally tangent to a circle ω at point...
Category: Geometry
Problem
Circles ω1 and ω2 with centres O1 and O2 are externally tangent at point D and internally tangent to a circle ω at points E and F, respectively. Line t is the common tangent of ω1 and ω2 at D. Let AB be the diameter of ω perpendicular to t, so that A, E and O1 are on the same side of t. Prove that lines AO1, BO2, EF and t are concurrent. (Brasil)