### Three Balls

A circle has centre O and angle POR = angle QOR. Construct tangents at P and Q meeting at T. Draw a circle with diameter OT. Do P and Q lie inside, or on, or outside this circle?

### Mouhefanggai

Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.

### When the Angles of a Triangle Don't Add up to 180 Degrees

This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the triangle.

# Ball Packing

##### Age 14 to 16 Challenge Level:

 If a ball is rolled into the corner of a room how far is its centre from the corner? A sphere of diameter $10$cm is packed into a cubic box whose internal side lengths are $12$cm. To prevent the sphere from rolling around 8 identical smaller spheres are placed in the corners of the box. What is the radius of one of the smaller spheres?