Final answer:
To prove that all circles are similar, we compare the ratios of the radii and the distances from the centers to the circumference. In this case, the ratio is the same, so the circles are similar.
Step-by-step explanation:
In order to prove that all circles are similar, we need to show that the ratio of any two corresponding lengths in the circles is the same. Let's compare the radii of circle A and B. The radius of circle A is 3, while the radius of circle B is 6. The ratio of the radii is 3/6 = 1/2.
Now let's compare the distances from the centers of the circles to any point on the circumference. The distance from the center of circle A to a point on the circumference is always 3 units, while the distance from the center of circle B to a point on the circumference is always 6 units. The ratio of these distances is also 1/2.
Therefore, since the ratio of the radii and the distance from the centers to the circumference is the same, we can conclude that all circles are similar.