### 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

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

### At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

# Where Is the Dot?

##### Stage: 4 Challenge Level:

This problem offers students an opportunity to apply Pythagoras' Theorem.

It can also be used as a starting point for trigonometry:
• what happens to the height of the dot during the first $90^{\circ}$ of turn?
• what happens to the height of the dot when it turns beyond $90^{\circ}$?
• what can you say about the horizontal displacement of the dot as it turns through a full circle?