IMO 2006 Shortlist G1
Let ABC be a triangle with incentre I. A point P in the interior of the triangle satisfies ∠PBA + ∠PCA = ∠PBC + ∠PCB. Sh...
Category: Geometry
Problem
Let ABC be a triangle with incentre I. A point P in the interior of the triangle satisfies ∠PBA + ∠PCA = ∠PBC + ∠PCB. Show that AP ≥ AI and that equality holds if and only if P coincides with I. (Korea)