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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

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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?

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At a Glance

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

Kite in a Square

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

For Coordinates method:

  • what are the equations of the lines?
  • where do they intersect?

For Similar Figures method:

  • which angles are the same?
  • what lengths do we know?

For Pythagoras method:

  • where are the right angles?
  • what lengths do we know?