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the triangles A_1, B_1, C_1 & A_2, B_2, C_2 & A_3, B_3, C_3 have their corresponding...

the triangles A_1, B_1, C_1 & A_2, B_2, C_2 & A_3, B_3, C_3 have their corresponding sides parallel. Hence each pair of triangles has a center of perspectivity (assume that these centers of perspectivities exist). Prove that the three centers of perspectivities are collinear.

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