Enigma 1739: Dodecagarden
6 March 2013
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From New Scientist #2907, 9th March 2013 [link]
In our local park the “Dodecagarden” is fenced in by 12 straight fences: the shortest is 1 metre long and the longest is less than 100 metres long.
The 12 corners of the garden all lie on a circle whose radius is a whole number of metres, and the 12 angles made at the corners by the fences are all equal.
Some of the fences have been reclaimed from an earlier use. Three shortest fences once enclosed a triangular garden and three longest fences once enclosed another triangular garden. The area of the larger triangle was a whole number times the area of the smaller one.
How many times?
Enigma 1528 is also about cyclic polygons.