Homothetic center

Figure 1: The point O is an external homothetic center for the two triangles. The size of each figure is proportional to its distance from the homothetic center.

In geometry, a homothetic center (also called a center of similarity or a center of similitude) is a point from which at least two geometrically similar figures can be seen as a dilation or contraction of one another. If the center is external, the two figures are directly similar to one another; their angles have the same rotational sense. If the center is internal, the two figures are scaled mirror images of one another; their angles have the opposite sense.

Figure 2: Two geometric figures related by an external homothetic center S. The angles at corresponding points are the same and have the same sense; for example, the angles ABC, ∠A'B'C' are both clockwise and equal in magnitude.

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