1. Keep the white circle of inversion fixed.
Let A be a point (the blue); how many circles of center A are globally invariant?
Let the radius of the circle around A be fixed. How many circles of this radius are globally invariant?
Where are the centers of these globally invariant circles?
2. Move the point C counter-clockwise, how is C' moving?
Is your answer valid for every position of the blue circle?
Give a general rule.
When D is moving on the line, D' is moving on the black circle.
In your own meaning, what does it mean that D is moving in the positive sense?
How is D' moving when D is moving in the positive sense?
3. For a given blue line and a given blue circle, try to choose the white points in such a way that
D' is on the circle, D is on a black line (transformed from an originally black circle) and
both black lines are simultaneously on top of the blue ones.
Try to solve the problem in the three relative positions of the blue line and the blue circle.
What are the 3 possible relative positions?
4. Given a line g and a circle G, is it always possible to find an inversion f such that f(g) = G?