Constructions of the inversion of a point P in a circle
In each of these figures, it is alleged that the point Q is the inversion of
point P in the red circle (and vice versa). Give reasoning that shows this
is true and also answer the following questions.
Questions
- In each case, give reasoning to explain why Q is the inversion of P, based
on the definition of inversion.
- In each case, explain how one can start with the circle and P exterior to
the circle and construct Q.
- In each case, explain how one can start with the circle and Q interior to
the circle and construct P.
- For which of the constructions does the construction of Q work even when
P is interior to the circle as well as exterior (so it would work as a single
Sketchpad construction of the inversion of P)?
- Which is your favorite or your candidate for simplest and easiest construction
of the inversion of P for the two cases: P exterior and P interior?
