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    Geometric Series : Infinite Series of Circles inside Equilateral Triangles

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    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?

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    Problem:

    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 previous area.
    What is the sum of all of the shaded areas?

    Solution:

    If (a1) is the side of the equilateral triangle inscribed in circle (R1), then
    ...

    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.

    $2.49

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