Inversion Construction Methods

These methods are taken from Lab 6 and from the reading in Ogilvy and also from Sved.

  1. Use the definition of inversion to prove that in each figure the point Q is the inversion of point P in circle c with center O.  These figures provide several practical methods for constructing inverses with straightedge and compass.
  2. Tell which of these constructions work with P inside the circle.
  3. Be prepared to invert any point P in a given circle with straightedge and compass.

Figure 1: Compass only!

Figure 2.  Uses a line instead of one circle.

Figure 3: Uses tangent PT.  Was PA tangent in figures 1 and 2?

Figure 4: This construction was invented by a 444-5 student a few years ago.

Figure 5: This figure uses stereographic projection to connect inversion with reflection in the equatorial circle.

Figure 6.  This is a more efficient construction that uses the same geometry as Figure 5.