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209

Part of 1975 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 209 All Soviet Union MO 1975 area of midpointsof diagonals in convex hexagon

Source:

7/5/2019
Denote the midpoints of the convex hexagon A1A2A3A4A5A6A_1A_2A_3A_4A_5A_6 diagonals A6A2A_6A_2, A1A3A_1A_3, A2A4A_2A_4, A3A5A_3A_5, A4A6A_4A_6, A5A1A_5A_1 as B1,B2,B3,B4,B5,B6B_1, B_2, B_3, B_4, B_5, B_6 respectively. Prove that if the hexagon B1B2B3B4B5B6B_1B_2B_3B_4B_5B_6 is convex, than its area equals to the quarter of the initial hexagon.
geometryareashexagondiagonal