$$ 7. Prove that inversion in the unit circle maps the circle $(x-a)^{2}+(y- b)^{2}=r^{2}$ to the circle \left(x-\frac{a}{d} ight)^{2}+\left(y-\frac{b}{d} ight)^{2}=\left(\frac{r} {d} ight)^{2} $$ where $d=a^{2}+b^{2}-r^{2}$, provided that $d eq 0$ CS.JG.058