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Puzzle of the Week

This is a slight variant of the puzzle of the previous week.
Let the center of a regular polygon be defined as the point of intersection of all the straight lines which bisect the internal angles of its vertices. Let R be the ratio of the shortest distance between the center and any vertex and the shortest distance between the center and any side of the polygon.

Consider a regular polygon whose R is less than 1.1. However, its R is less than that of another regular polygon which has one side less, by more than 2%.

What is the shape of the first regular polygon?


Last date for submitting answers: 23 September 2012

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