331
Introduction to Inversion
r2
h
r2
r1 r1
Figure 10.17. The relationships needed to show that r 2 = r/3 (equation (14). Note that h = r − 2r 2 = 2r 1 − 2r 2, where the last equality follows because r = 2r 1.
x = r − 2r − t1 2
r2
t1
r1+ t1
r1
Figure 10.18. The relationships needed to show that t 1 = r/15 [equation (15)].
We now begin to invert the figure with respect to the point T, chosen as shown in figure 10.19. For simplicity we can take the radius of the inversion circle Σ to be k = 1 (which only means that everything is scaled to 1). Then, by the definition of inversion, we must have for point O TO ⋅ TO′ = 1.