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Area is at least .....

Source: India National Olympiad 2003, Problem 5

October 10, 2005

geometryarea of a triangleHeron's formulageometry solved

Problem Statement

Let a, b, c be the sidelengths and S the area of a triangle ABC. Denote

x=a+\frac{b}{2}

y=b+\frac{c}{2}

and

z=c+\frac{a}{2}

. Prove that there exists a triangle with sidelengths x, y, z, and the area of this triangle is

\geq\frac94 S