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Inequality in a cyclic quad

Source: St Petersburg 2021 9.3

December 23, 2021
geometry

Problem Statement

Given is cyclic quadrilateral ABCDABCD with∠A=3A = 3∠BB. On the ABAB side is chosen point C1C_1, and on side BCBC - point A1A_1 so that AA1=AC=CC1AA_1 = AC = CC_1. Prove that 3A1C1>BD3A_1C_1>BD.
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