MathDB

2

Part of 2006 Mediterranean Mathematics Olympiad

Problems(1)

Area Inequality

Source: Mediterranean MO 2006

10/30/2010
Let PP be a point inside a triangle ABCABC, and A1B2,B1C2,C1A2A_1B_2,B_1C_2,C_1A_2 be segments passing through PP and parallel to AB,BC,CAAB, BC, CA respectively, where points A1,A2A_1, A_2 lie on BC,B1,B2BC, B_1, B_2 on CACA, and C1,C2C_1,C_2 on ABAB. Prove that Area(A1A2B1B2C1C2)≥12Area(ABC) \text{Area}(A_1A_2B_1B_2C_1C_2) \ge \frac{1}{2}\text{Area}(ABC)
geometryinequalitiesparallelogramgeometry proposed