Supplementary Investigation 25

Finding a Circle of Inversion Given Two Points

Tool(s) Geometers Sketchpad

Data File(s) si25

Focus Given two points, it is possible to find more than one circle of inversion for which the two points are inverses of one another.

Tasks

1. Given points P and P', find two circles with centers O and O' and radii r and r' respectively for which OP*OP' = r² and O'P*O'P' = r'².

2. Explore methods for finding circles of inversion involving more than "guess and check" strategies. Discuss your findings.

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