### Some(?) of the Parts

A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle

### 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?

### Logosquares

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.

# Rectangular Pyramids

### Why do this problem?

It provides experience of generalising a result from 2 dimensions to an equivalent result in 3 dimensions. This problem asks the question for them but learners should be encouraged to ask themselves "What if..." and always to think about possible generalisations.

### Key questions

What comes to mind when a problem involves squares of distances?
If we are looking for Pythagoras theorem where are the right angles triangles?

### Possible extension

The problem Pythagoras for a Tetrahedron.