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Circles Ad Infinitum
Age 16 to 18
Challenge Level 
A circle of radius 1 cm is inscribed in an equilateral triangle. A smaller circle is inscribed at each vertex touching the first circle and tangent to the two 'containing' sides of the triangle. This process is continued ad infinitum....
What is the sum of the circumferences of all the circles?
What is the sum of their areas?
Adding all the circumferences or adding all the areas, which sum grows faster?
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