Convex pentagon and areas of triangles
Source: Ukrainian TST 2008 Problem 11
February 12, 2009
geometrytrapezoidsymmetrygeometry unsolved
Problem Statement
Let be convex pentagon such that S(ABC) \equal{} S(BCD) \equal{} S(CDE) \equal{} S(DEA) \equal{} S(EAB). Prove that there is a point inside pentagon such that S(MAB) \equal{} S(MBC) \equal{} S(MCD) \equal{} S(MDE) \equal{} S(MEA).