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## 'Medallions' printed from http://nrich.maths.org/

I keep three circular medallions in a rectangular box in which
they just fit with each one touching the other two. The smallest
one has radius $4$ cm and touches one side of the box, the middle
sized one has radius $9$ cm and touches two sides of the box and
the largest one touches three sides of the box. What is the radius
of the largest one? [This problem by R B J T Allenby appeared in
the Sunday Times on 12.11.00.]