MATLAB Question

Take a circle of radius 1.

Within the circle, inscribe an equilateral triangle. Then, within the triangle, inscribe a new smaller circle.

Within the smaller circle inscribe a regular square, and within the square, inscribe yet another circle.

Within the smaller circle inscribe a regular pentagon, and within the pentagon, inscribe yet another circle.

Iterate this process of inscribing regular polygon and a new smaller circle, increasing the number of sides of the polygon by 1 each time.

What is the radius of the limiting circle?