A circle is inscribed within an equilateral triangle. A smaller circle is inscribed in the space between the circle and two edges of the equilateral triangle. If the radii of the large and small circles are and respectively, what is the value of ?
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http://calculus-geometry.hubpages.com/hub/Inscribed-Circles-and-Equilateral-Triangles-7-Hard-Geometry-Problems-and-Solutions