Problem of the Week 999

Japanese Circles

What is the radius of each of the two large circles? The radius of the sector is 1 and all apparent tangencies, symmetries, and congruences are true. So there are exactly three sizes of full circles shown.

Source: This was a Japanese Temple Problem, and was published in 1833 by Shin Oh Jiku. The problem is one of many beautiful problems in the new MAA book by Ross Honsberger titled "Mathematical Diamonds."

© Copyright 2004 Stan Wagon. Reproduced with permission.