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?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.