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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

Ladder and Cube

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?

Age 14 to 16
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?