You may also like

problem icon

Lunar Angles

What is the sum of the angles of a triangle whose sides are circular arcs on a flat surface? What if the triangle is on the surface of a sphere?

problem icon


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?

problem icon

Baby Circle

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?


Age 16 to 18 Challenge Level:

Two circles of equal size intersect and the centre of each circle is on the circumference of the other.


What is the area of the intersection?

Now imagine that the diagram represents two spheres of equal volume with the centre of each sphere on the surface of the other.

What is the volume of intersection?