Problem

Source: 2010 Saudi Arabia BMO TST 3.2 - Balkan

Tags: ratio, equal areas, geometry, Cevians



Consider a triangle ABC and a point P in its interior. Lines PA, PB, PC intersect BC, CA, AB at A,B,C , respectively. Prove that BABC+CBCA+ACAB=32if and only if at least two of the triangles PAB, PBC, PCA have the same area.