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Let A_1A_2 \ldots A_n be a convex polygon, n \geq 4. Prove that A_1A_2 \ldots A_n is cyclic if and only if to each vertex A_j one can assign a pair (b_j, c_j) of real numbers, j = 1, 2, \ldots, n, so that A_iA_j = b_jc_i - b_ic_j for all i, j with 1 \leq i < j \leq n.

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