MathDB

363

Part of 1983 All Soviet Union Mathematical Olympiad

Problems(1)

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

Source:

7/28/2019
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?
geometryareasareaequal areas