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
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?
Two smaller circles, centres $B$ and $C$ touch each other
externally and touch the circle centre $A$ internally.
What happens to the perimeter of triangle $ABC$ as the two
smaller circles roll around touching the inside rim of the bigger
circle or as the two smaller circles vary in size?
Move the sliders to change the radii of the smaller circles and
drag the point $B$ to move the circles.
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