Area of Infinite Pointed Star

Geometry Level pending

Suppose we have 2 concentric circles with radii \(r\) and \(\frac{r}{n}\) for some integer \(n \geq 2\). Place \(n\) equally spaced points on the circumference of the larger circle. For each such point, draw two tangent line segments to the smaller circle and shade in the area enclosed by the new line segments and the smaller circle.

As \(n\) tends to infinity, what portion of the larger circle do we shade with the above construction?

CLARIFICATION: once a region is shaded, shading it again has no effect.

note: sorry there's no picture... message me if you know of a good site to draw geometry and export images!


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