area of triangles
Source: Russian 2007
September 17, 2007
geometrygeometry proposed
Problem Statement
Two triangles have equal longest sides and equal smallest angles. A new triangle is constructed, such that its sides are the sum of the longest sides, the sum of the shortest sides, and the sum of the middle sides of the initial triangles. Prove that the area of the new triangle is at least twice as much as the sum of the areas of the initial ones.