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TOT 107 1986 Spring J1 3 out of 4 regions have equal areas

Source:

August 29, 2019

geometryequal areasareas

Problem Statement

Through vertices

A

and

B

of triangle

ABC

are constructed two lines which divide the triangle into four regions (three triangles and one quadrilateral). It is known that three of them have equal area. Prove that one of these three regions is the quadrilateral .
(G . Galperin , A . Savin, Moscow)

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