Compare Areas
This problem brings together ideas of areas of circles and squares,
the use of Pythagoras theorem and the property of tangents to a
circle from an exernal point.
Possible approach
You might start with the middle diagram which is the easiest. It
brings in the ratio of the sides of an isosceles right angles
triangle which is again used in the other two parts.
Key questions
If you know the side length of an isosceles right angled triange
how do you find the hypotenuse?
Which lengths are equal in the digram?
Which angles are equal?
Can you use the symmetry of the diagram?
Possible extension
The problem
Circle-in also uses one of the circle theorems (the tangent is
perpendicular to the radius at the point of contact).