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A triangle \(A B C\) is given. Points \(A_1, A_2, B_1, B_2, C_1, C_2\) are taken on the rays \(B A, C A, C B, A B, A C, B C\) respectively such that \(A A_1=A A_2=B C, B B_1=B B_2=\) \(C A\), and \(C C_1=C C_2=A B\). Prove that the area of the hexagon \(A_1 A_2 B_1 B_2 C_1 C_2\) is at least 13 times the area of the triangle \(A B C\).
in Mathematics by Platinum (138,598 points) | 25 views

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