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Explanation of the construction: Given a circle of center B radius R and a point A, the inversion of A wrt the circle is the point C on the same ray from B as A such that the circle radius is the geometric mean of the distances of A and C from B, that is, BA*BC = R^2. The construction on this page uses similar right triangles ABD and DBE to get the equal ratios of short to long legs, BA/R = R/BE, which gives BE as the desired distance BC.

To use create Inversion as a Sketchpad tool:

  1. Do the construction shown on this page in Sketchpad.
  2. "Select" point A, point B, the circle, and point C simultaneously in succession.
  3. Click Sketchpad's Custom Tool button (looks like a double wedge).
  4. Select "Create new tool" and name it Inversion.
  5. To use the Inversion tool. click on the Custom Tool button, and click on the equivalents of A, B, and the circle as it prompts you in the tiny lower left message box.

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