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 AA1⋅AA2+BB1⋅BB2+CC1⋅CC2≥19(AB2+BC2+CA2)
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 AA1⋅AA2+BB1⋅BB2+CC1⋅CC2≥19(AB2+BC2+CA2)