Homothetic Center - Circles

Circles

Circles are geometrically similar to one another and mirror symmetric. Hence, a pair of circles has both types of homothetic centers, internal and external, unless the centers are equal or the radii are equal; these exceptional cases are treated after general position. These two homothetic centers lie on the line joining the centers of the two given circles, which is called the line of centers (Figure 3). Circles with radius zero can also be included (see exceptional cases), and negative radius can also be used, switching external and internal.

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