A spiropath is a sequence of connected line segments end to end
taking different directions. The same spiropath is iterated. When
does it cycle and when does it go on indefinitely?

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?

Circles in Circles

Age 16 to 18 Challenge Level

Draw lines through the centres of the circles. Write down and
solve some simple equations involving the radii. Remember to use
the exact values involving square roots (irrational numbers).