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.