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Keep expanding squares outside

Source: Indonesian Mathematical Olympiad 2013 Problem 7

September 5, 2013
geometry unsolvedgeometry

Problem Statement

Let ABCDABCD be a parallelogram. Construct squares ABC1D1,BCD2A2,CDA3B3,DAB4C4ABC_1D_1, BCD_2A_2, CDA_3B_3, DAB_4C_4 on the outer side of the parallelogram. Construct a square having B4D1B_4D_1 as one of its sides and it is on the outer side of AB4D1AB_4D_1 and call its center OAO_A. Similarly do it for C1A2,D2B3,A3C4C_1A_2, D_2B_3, A_3C_4 to obtain OB,OC,ODO_B, O_C, O_D. Prove that AOA=BOB=COC=DODAO_A = BO_B = CO_C = DO_D.
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