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MMO 242 Moscow MO 1953 regular star-shaped pentagon, areas

Source:

August 9, 2019
pentagonequal areasareasgeometry

Problem Statement

Let AA be a vertex of a regular star-shaped pentagon, the angle at AA being less than 180o180^o and the broken line AA1BB1CC1DD1EE1AA_1BB_1CC_1DD_1EE_1 being its contour. Lines ABAB and DEDE meet at FF. Prove that polygon ABB1CC1DED1ABB_1CC_1DED_1 has the same area as the quadrilateral AD1EFAD_1EF.
Note: A regular star pentagon is a figure formed along the diagonals of a regular pentagon.
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