Answer:
1) Use translation to coincide the center of a circle with the center of the other circle.
2) We construct the respective loci for the circles.
3) Compare each loci by direct inspection (
must be the same and radii must be different but constant) to conclude the similarity of the two circles.
Explanation:
Geometrically speaking, a circle is formed after knowing its center and radius.
1) Use translation to coincide the center of a circle with the center of the other circle. In this case, we translate the center (
) of the circle A to the location of the center of the circle B (
):
![C_(A') (x,y) = (6,7) + [(2,4) - (6,7)]](https://img.qammunity.org/2022/formulas/mathematics/high-school/5bxdegqx2fqmkm1lbheuydvg5qhwb8ep4k.png)

2) We construct the respective loci for the circles.
By Analytical Geometric, a circle is represented by the following locus:

Where:
- Coordinates of a point of the circunference.
- Coordinates of the center of the circle.
- Radius of the circle.
3) Compare each loci by direct inspection (
must be the same and radii must be different but constant) to conclude the similarity of the two circles.
Then, the circles A' and B are represented by the following loci:
Circle A'

Circle B

Since both the
component of each circle is the same and radii are different but constant, then we conclude that circle A is similar to circle B.