You can prove that two circles are similar to each other because the ratio of radius to radius taken anywhere within two circles is uniform. What is the process of growing or shrinking a circle from one to the other called?

The process of growing or shrinking a circle from one to another while maintaining the same shape is called dilation. Dilation is a type of transformation in which the size of a figure is changed by a scale factor without altering its shape. In the case of circles, dilation involves changing the radius of the circle while keeping the proportions of the circle intact.