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is pentagon convex? - All-Russian MO 1998 Regional (R4) 10.6

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September 17, 2024
geometrypentagonconvex

Problem Statement

The pentagon A1A2A3A4A5A_1A_2A_3A_4A_5 contains bisectors ℓ1\ell_1, ℓ2\ell_2, ......, ℓ5\ell_5 of angles ∠A1\angle A_1, ∠A2\angle A_2, ... ... , ∠A5\angle A_5 respectively. Bisectors ℓ1\ell_1 and ℓ2\ell_2 intersect at point B1B_1, ℓ2\ell_2 and ℓ3\ell_3 - at point B2B_2, etc., ℓ5\ell_5 and ℓ1\ell_1 intersect at point B5B_5. Can the pentagon B1B2B3B4B5B_1B_2B_3B_4B_5 be convex?
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