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concurrent, broken line bisectors - All-Russian MO 1997 Regional (R4) 9.7

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September 23, 2024
geometryconcurrencyconcurrent

Problem Statement

Given triangle ABCABC. Point B1B_1 bisects the length of the broken line ABCABC (composed of segments ABAB and BCBC), point C1C_1 bisects the length of the broken lineACBACB, point A1A_1 bisects the length of of the broken line CABCAB. Through points A1A_1, B1B_1 and C1C_1 straight lines ℓA\ell_A ,ℓB\ell_B, ℓC\ell_C are drawn parallel to the bisectors angles BACBAC, ABCABC and ACBACB respectively. Prove that the lines ℓA\ell_A, ℓB\ell_B and ℓC\ell_C intersect at one point.
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