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
What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
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?
The diagram shows two circles and four equal semi-circular arcs. The area of the inner shaded circle is $1$. What is the area of the outer circle?
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.