Problem

Source: 4th Iranian Geometry Olympiad (Advanced) P4

Tags: IGO, Iran, geometry



Three circles ω1,ω2,ω3 are tangent to line l at points A,B,C (B lies between A,C) and ω2 is externally tangent to the other two. Let X,Y be the intersection points of ω2 with the other common external tangent of ω1,ω3. The perpendicular line through B to l meets ω2 again at Z. Prove that the circle with diameter AC touches ZX,ZY. Proposed by Iman Maghsoudi - Siamak Ahmadpour