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triangle inscribed in triangle

Source: Polish MO Finals 1965 p5

August 30, 2024
geometryinsscribedareas

Problem Statement

Points A1 A_1 , B1 B_1 , C1 C_1 divide respectively the sides BC BC , CA CA , AB AB of the triangle ABC ABC in the ratios k1 k_1 , k2 k_2 , k3 k_3 . Calculate the ratio of the areas of triangles A1B1C1 A_1B_1C_1 and ABC ABC .
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