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?
problem could work well as a 'poster' - a visual challenge
placed where students will see it. Or presented at the end of a
lesson as something to try to solve.
This problem can worked well as something short and closed, but
there is also an opportunity to invite questions which open up
beyond the initial challenge. Finding the area of a square in a
quadrant or squares fitted in the space between either of the two
squares in the main problem and the circle.
The approach suggested above indicates one route to extension
within this context, or for another challenge fitting squares into
shapes try Squirty.
Semi-square offers another opportunity to work out areas of
squares inside circles.
Squares could be an excellent and accessible challenge for
slightly less experienced students.