MathDB
S_{B_1..B_6}<= 3/2 S_{A_1...A_6} , hexagons 1984 Kyiv City MO 10.5

Source:

July 15, 2021
geometrygeometric inequalityhexagon

Problem Statement

The vertices of a regular hexagon A1,A2,...,A6A_1,A_2,...,A_6 lie respectively on the sides B1B2B_1B_2, B2B3B_2B_3, B3B4B_3B_4, B4B5B_4B_5, B5B6B_5B_6, B6B1B_6B_1 of a convex hexagon B1B2B3B4B5B6B_1B_2B_3B_4B_5B_6. Prove that SB1B2B3B4B5B6≤32SA1A2A3A4A5A6.S_{B_1B_2B_3B_4B_5B_6} \le \frac32 S_{A_1A_2A_3A_4A_5A_6}.
Back to ProblemsView on AoPS