Java Applet Demonstrating the Construction of a p-line.
In the following applet, all of the steps for finding the inverse of a point are shown.  Using the inverse and the other two points to find the circle incident with the three points is not displayed.  The construction is color coded.  The meaning for each color is listed below.  The letters in parenthesis are consistent with those used in the explanation of the construction.
  • Green Ray (R) - starts at the center of the circle and travels through the point (P) in which we are looking for its inverse.
  • Blue Line - Perpendicular to ray through P.  Intersects O at two points, T and U.
  • Red Rays - Radii of the circle (O) intersecting the circle at T and U.
  • Yellow Lines - Perpendiculars to radii at T and U.
  • Purple Point - The inverse of P, P'.

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*Note: The preceding applet was developed using the JavaSketchPad.