MathDB
2015 Team #11

Source:

August 3, 2022
2015team test

Problem Statement

Let ABCDEFABCDEF be a regular hexagon, and let GG, HH, II, JJ, KK, and LL be the midpoints of sides ABAB, BCBC, CDCD, DEDE, EFEF, and FAFA, respectively. The intersection of lines AH‾\overline{AH}, BI‾\overline{BI}, CJ‾\overline{CJ}, DK‾\overline{DK}, EL‾\overline{EL}, and FG‾\overline{FG} bound a smaller regular hexagon. Find the ratio of the area of the smaller hexagon to the area of ABCDEFABCDEF.
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