| The fixed white circle is the circle of inversion. | The blue circle is variable. |
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1.
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. |
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2. Keep the white circle of inversion fixed.
How many circles (the blue ones) of center A are globally invariant? |
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3. Let the radius of the circle around A be fixed.
How many circles of this radius are globally invariant? |
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4. The radius of the white circle of inversion is k and the radius of the blue inversed circle is r.
Where are the centers of the globally invariant circles of Problem 3 above? |
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5.
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? |
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6. For a given blue line and a given blue circle, try to choose the white
circle of inversion in such a way that
a) D' is on the circle,
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? |
| 7. Given a line g and a circle G, is it always possible to find an inversion f such that f(g) = G? |