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?

Spokes

Age 16 to 18 Challenge Level:

Draw three equal line segments in a unit circle so that they
divide the disc into four parts of equal area.