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XA_i=A_{i+2}A_{i+3} inside a convex pentagon

Source: Belarus TST 2009 8.2

June 13, 2020
pentagonequal segmentsgeometry

Problem Statement

Does there exist a convex pentagon A1A2A3A4A5A_1A_2A_3A_4A_5 and a point XX inside it such that XAi=Ai+2Ai+3XA_i=A_{i+2}A_{i+3} for all i=1,...,5i=1,...,5 (all indices are considered modulo 55) ?
I. Voronovich
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