IMO 2006 Shortlist G8
Let ABCD be a convex quadrilateral. A circle passing through the points A and D and a circle passing through the points ...
Category: Geometry
Problem
Let ABCD be a convex quadrilateral. A circle passing through the points A and D and a circle passing through the points B and C are externally tangent at a point P inside the quadrilateral. Suppose that ∠PAB + ∠PDC ≤ 90◦ and ∠PBA + ∠PCD ≤ 90◦ . Prove that AB + CD ≥ BC + AD. (Poland)