Set the set right!

Geometry Level 4

\(\{A\}\) is the largest possible set consisting of numbers selected from \(\{1, 2, 3,\ldots,2015\}\) such that any two elements in \(\{A\}\) can define the lengths of an isosceles triangle, each playing the role of either base or the two equal sides.

If the largest and smallest elements in \(\{A\}\) are selected to form the lengths of an isosceles triangle (with the largest element as the measure of the equal sides), what is the difference between the circumference of the circle which can be inscribed in this triangle and the the largest number in \(\{A\}\) (round to nearest whole number)?

This problem was adapted from the 2016 SMO Junior Round 2.

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