A regular hexagon and two equals angles. What is blue : green : red?

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## Solution

Blue : green : red is 1 : 3 : 7.

The orange triangle ABG is similar and twice as large as the two triangles GCH (green) and HKN (blue). It is clear than N is on the diagonal AD and DN = AD/8. Also, it is clear that AHN is isosceles, so the red sides are equal. If AB = 4, then the problem’s Green length = HC = 1, Blue = HD = 3, and Red = 7.

## Video

Please find here the video solution: Video: Hex division II.