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'Salinon' printed from http://nrich.maths.org/
Why do this
The solution uses the formula for the area of a circle and gives
practice in geometrical reasoning and manipulating algebraic
Start with a class discussion about the radii of the 4 semi-circles
and the circle on AB as diameter. When the students have understood
that there are only two unknowns involved, and the other radii can
all be expressed in terms of the two unknowns, then they are ready
to write down the areas and answer the question which they could do
Dynamic geometry software could be a useful tool to aid
investigation but this is not essential.
If the blue semicircles have radii a and b what can you say about
the other radii?
Round and Round
is a similar problem.
Learners could make up their own problems of this type.