MathDB
2018 IGO Elementary Level P2

Source:

September 20, 2018
IGO2018 igoIrangeometry

Problem Statement

Convex hexagon A1A2A3A4A5A6A_1A_2A_3A_4A_5A_6 lies in the interior of convex hexagon B1B2B3B4B5B6B_1B_2B_3B_4B_5B_6 such that A1A2B1B2A_1A_2 \parallel B_1B_2, A2A3B2B3A_2A_3 \parallel B_2B_3,..., A6A1B6B1A_6A_1 \parallel B_6B_1. Prove that the areas of simple hexagons A1B2A3B4A5B6A_1B_2A_3B_4A_5B_6 and B1A2B3A4B5A6B_1A_2B_3A_4B_5A_6 are equal. (A simple hexagon is a hexagon which does not intersect itself.)
Proposed by Hirad Aalipanah - Mahdi Etesamifard