A small circle fits between two touching circles so that all three
circles touch each other and have a common tangent? What is the
exact radius of the smallest circle?
Two semicircle sit on the diameter of a semicircle centre O of
twice their radius. Lines through O divide the perimeter into two
parts. What can you say about the lengths of these two parts?
Ten squares form regular rings either with adjacent or opposite
vertices touching. Calculate the inner and outer radii of the rings
that surround the squares.
Congratulations Tom Davie, Mike Gray and Ella Ryan of Madras
College for your excellent team work on this problem. This is their
solution; Tom wrote up the first part, Mike solved the equation and
showed that there are two possible circles, and Ella described the
construction of the smallest circle. Work like this is a real
pleasure to read.