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ASU 363 All Soviet Union MO 1983 equal areas inside a triangle

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July 28, 2019
geometryareasareaequal areas

Problem Statement

The points A1,B1,C1A_1,B_1,C_1 belong to [BC],[CA],[AB][BC],[CA],[AB] sides of the ABCABC triangle respectively. The [AA1],[BB1],[CC1][AA_1], [BB_1], [CC_1] segments split the ABCABC onto 44 smaller triangles and 33 quadrangles. It is known, that the smaller triangles have the same area. Prove that the quadrangles have equal areas. What is the quadrangle area, it the small triangle has the unit area?
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