Ken's POTW

Olympic Ring Addition
Given the five olympic rings how can the digits one through nine be placed within the nine regions (five non-overlapping ring regions and four overlapping regions shared between two rings) so that each ring contains the same total?

Or alternatively, using the labels A through I for the regions, how can the numbers one through nine be assigned to the variables such that:

A+B = B+C+D = D+E+F = F+G+H = H+I

Is there a logical approach other than brute force?

Source: Andrew Gray in newsgroup rec.puzzles, March 23, 1997.

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