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?
Prove that the shaded area of the semicircle is equal to the
area of the inner circle.
What percentage of the sector OAB is taken up with the inner
What happens if angle AOB is less than 90°
or between 90 and 180 degrees?