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?
James of Christ Church Cathedral School, Oxford and Alexander from Shevah-Mofet School, Israel sent very good solutions to this question.
Here is another method for Circle Packaging from Suzanne and Nisha of the Mount School, York: