Supplementary Investigation 24

Inverse Points and Orthogonal Circles

Tool(s) Geometers Sketchpad

Data File(s) si24

Focus The intersection points of two circles, each orthogonal to the circle of inversion, are inverse points relative to the circle of inversion.

Tasks

1. Explain the basis for the construction of the orthogonal circles shown above.

2. Move the drag pts and observe the range of motions available to P and P'. Under which circumstances do you obtain the widest range of separations between P and P'?

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