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?
Two circles with radii 1cm and 4cm touch. The point P is on the smaller circle, Q is on the larger circle, and PQ is a tangent to both circles. What is the length of PQ?
This problem is taken from the UKMT Mathematical Challenges.