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Problem of the Week 944

Seventeen Circles

Take a circle and inscribe 4 interior-disjoint congruent circles A, B, C, D that are cyclically tangent (A is tangent to B is tangent to C is tangent to D is tangent to A), and so that each is tangent to the large circle. Then, in each of these four, inscribe four congruent tangent circles in exactly the same way, to get 16 small circles. Finally, inscribe a small circle C17 in the space around the center of the large circle and tangent to each of A, B, C, D. Which is larger, C17 or one of the sixteen circles inside A, B, C, D?

Source: Peter Woo, in Mathematics and Informatics Quarterly, vol. 11, No. 2, June 2001, p. 75.
© Copyright 2001 Stan Wagon. Reproduced with permission.

16 October 2001