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## 'Salinon' printed from http://nrich.maths.org/

Why do this
problem?
The solution uses the formula for the area of a circle and gives
practice in geometrical reasoning and manipulating algebraic
expressions.

Possible approach
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
individually.

Dynamic geometry software could be a useful tool to aid
investigation but this is not essential.

Key questions
If the blue semicircles have radii a and b what can you say about
the other radii?

Possible support
Try

Round and Round
Possible extension
Shaded Circles is a similar problem.

Learners could make up their own problems of this type.