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area ratio, configuration with three squares

Source: Mongolia 1999 Grade 8 P3

May 4, 2021
geometry

Problem Statement

Three squares ABB1B2,BCC1C2,CAA1A2ABB_1B_2,BCC_1C_2,CAA_1A_2 are constructed in the exterior of a triangle ABCABC. In the exterior of these squares, another three squares A1B2B3B4,B1C2C3C4,C1A2A3A4A_1B_2B_3B_4,B_1C_2C_3C_4,C_1A_2A_3A_4 are constructed. Prove that the area of a triangle with sides C3A4,A3B4,B3C4C_3A_4,A_3B_4,B_3C_4 is 1616 times the area of △ABC\triangle ABC.
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