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Geometric Series : Infinite Series of Circles inside Equilateral Triangles

An equilateral triangle is inscribed in a circle of radius 100. The area of the circle which lies outside of the triangle is shaded. The process continues to infinity.

What is the radius for the second area/ third area/ fourth area?

Side of first area/ side of second area/ side of third area/ side of fourth area?

Area of first area is ________, area of second area is _________, area of third area is ______________, area of fourth area is __________

Each new area is ___________of the prevous area. What is the sum of all of the shaded areas?

Solution Summary

A recursive expression is found for the area outside a triangle but inside a circles for an infinite set of triangles and circles. The solution is detailed and well presented. Diagrams are included.