Circumscribed To Infinity

Geometry Level 5

Circumscribe a triangle about a unit circle, another circle around the triangle, a square outside this circle, another circle outside the square and so forth.

Let \(r\) be the radius of the circle formed when the process is carried forever.

Find the square root of the sum of first 14 decimal places of \(r\)

You are allowed to compute the answer by calculator or software.


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