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