Inversion is a plane transformation determined by a fixed point S, which is called center of inversion and by a real number c called inversion constant. Each point on the circle of radius \(r{_{s}}= \sqrt{c}\) centered at point S is mapped, by inversion, into itself, so we can say that the inversion is uniquely determined by a circle \(k(s,r{_{s}})\) which is called a circle of inversion. Inversion is a plane transformation which set of lines and circles maps to the same set or it can replicate the line to a circle and vice versa. Lines through the center of inversion S, by inversion replicate themselves while the other lines replicate into a circles that does not pass the center S. Circles passing through the center S are mapped, by the inversion, in a lines that does not pass the center S, and the other circles are mapped into a circles, which also does not undergo inversion center S. By using the inversion we have proved on of the most beautiful theorem in geometry of triangle, the Feuerbach’s theorem. It claims that the Euler circle of any triangle is tangent internally to the incircle and tangent externally to the three escribed circles. Further, in addition to the work, by applying inversion, we have proved the most general case of the Apollonius problem. Ptolemy’s and Euler’s theorem were also proved.