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
The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...
Two semicircle sit on the diameter of a semicircle centre O of
twice their radius. Lines through O divide the perimeter into two
parts. What can you say about the lengths of these two parts?
This problem is taken from the UKMT Mathematical Challenges.