If two similar figures lie in the plane but do not have parallel sides (i.e., they are similar but not homothetic), there exists a center of similitude, also called a self-homologous point, which occupies the same homologous position with respect to the two figures (Johnson 1929, p. 16).
The similitude center 
of two triangles 
and 
can be constructed by extending each pair of corresponding sides of the triangles
and locating their intersection, then drawing the circumcircle passing through two
corresponding vertices of the triangles and the point of intersection of the pair
of lines through corresponding sides that contain these points. Repeating for each
of the three vertices gives three circles that intersect in a unique point, as illustrated
above. This point is the similitude center 
(Johnson 1929).
The locus of similitude centers of two nonconcentric circles is another circle having the line joining the two homothetic centers as its diameter.
There are a number of interesting theorems regarding the similitude centers of three circles (Johnson 1929, pp. 151-152).
1. The external similitude centers of three circles are collinear.
2. Any two internal similitude centers are collinear with the third external one.
3. If the center of each circle is connected with the internal similitude center of the other three [sic], the connectors are concurrent.
4. If one center is connected with the internal similitude center of the other two, the others with the corresponding external centers, the connectors are concurrent.
The six centers of similitude of three circles taken by pairs are the vertices of a complete quadrilateral (Evelyn et al. 1974, pp. 21-22).
