Stage: 5 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?
Visualising. Inscribed circle. Pythagoras' theorem. Quadratic equations. Long problems. Infinite series. Scale factors. Geometric sequence. Mathematical reasoning & proof. Enlargements.
Published April 1999,November 2008,December 2008.
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