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? The area of a regular pentagon
looks about twice as a big as the pentangle star drawn within
it. Is it? Well done to Andrew (Wilson's School), Shibon (North
London Collegiate School), and Jonathan (Oakwood Park Grammar
School), who had the right answer to the situation when the
squares are parallel to the lines on the grid. Shibon concluded
that: Andrew sent us a good proof: For the situation when
squares make angles with the lines of the grid, we have a good
answer from Daniel