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?
Show that for any triangle it is always possible to construct 3
touching circles with centres at the vertices. Is it possible to
construct touching circles centred at the vertices of any polygon?
What do you notice about the quadrilateral PQRS as ABCD
Is the area of PQRS always the same fraction of the area of ABCD
and, if so, what is this fraction?
Try to prove your conjectures.
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