Similarity Point

External (or positive) and internal (or negative) similarity points of two Circles with centers $C$ and $C'$ and Radii $r$ and $r'$ are the points $E$ and $I$ on the lines $CC'$ such that

$${\it CE\over \it C'E}={r\over r'},$$

or

$${\it CI\over \it C'I}=-{r\over r'}.$$