Problem

Source: 2011 Balkan Shortlist G4 BMO

Tags: geometric inequality, geometry, incircle



Given a triangle ABC, the line parallel to the side BC and tangent to the incircle of the triangle meets the sides AB and AC at the points A1 and A2 , the points B1,B2 and C1,C2 are dened similarly. Show that AA1AA2+BB1BB2+CC1CC219(AB2+BC2+CA2)