Question

Please help! :')

Prove that the two circles shown below are similar. (10 points)

Circle X is shown with a center at negative 2, 8 and a radius of 6. Circle Y is shown with a center of 4, 2 and a radius of 3.

Answer 1

To prove that two circles are similar, we need to show that they have the same shape. This means that the ratio of the radii of the two circles is the same as the ratio of their corresponding diameters 1.
In this case, Circle X has a center at (-2, 8) and a radius of 6. Circle Y has a center at (4, 2) and a radius of 3. To show that these two circles are similar, we need to show that the ratio of their radii is the same as the ratio of their corresponding diameters 1.
The distance between the centers of Circle X and Circle Y is:
d = sqrt((4 - (-2))^2 + (2 - 8)^2) = sqrt(6^2 + (-6)^2) = sqrt(72)
The ratio of the radii of Circle X and Circle Y is:
r1/r2 = 6/3 = 2
The ratio of their corresponding diameters is:
d1/d2 = (2 * r1)/(2 * r2) = r1/r2 = 2
Since the ratio of their radii is the same as the ratio of their corresponding diameters, we can conclude that Circle X and Circle Y are similar 1.