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.](/Images/godic/202501/18/Homothetic_transformation.svg0817.png")
![The external (above) and internal (below) homothetic centers of the two circles (red) are shown as black points.](/Images/godic/202501/18/Point_circle0817.gif")
![Figure 3: Two circles have both types of homothetic centers, internal (I) and external (E). The radii of the circles (r1 and r2) are proportional to the distance (d) from each homothetic center. The points A1 and A2 are homologous, as are the points B1 and B2.](/Images/godic/202501/18/Circles_homothetic_centers.svg0817.png")
![Figure 4: Lines through corresponding antihomologous points intersect on the radical axis of the two given circles (green and blue). The points Q and P′ are antihomologous, as are S and R′. These four points lie on a circle that intersects the two given circles; the lines through the intersection points of the new circle with the two given circles must intersect at the radical center G of the three circles, which lies on the radical axis of the two given circles.](/Images/godic/202501/18/Two_circles_anti-homologous_points_radical_axis.svg0817.png")
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/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.