IMO 2008 Shortlist G7

Let ABCD be a convex quadrilateral with AB 6= BC. Denote by ω1 and ω2 the incircles of triangles ABC and ADC. Suppose th...

IMO 2008 Shortlist G7

Category: Geometry

Problem

Let ABCD be a convex quadrilateral with AB 6= BC. Denote by ω1 and ω2 the incircles of triangles ABC and ADC. Suppose that there exists a circle ω inscribed in angle ABC, tangent to the extensions of line segments AD and CD. Prove that the common external tangents of ω1 and ω2 intersect on ω.