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? This problem is taken from
the UKMT Mathematical Challenges.