Circle A has center of (6, 7), and a radius of 4 and circle B has a center of (2, 4), and a radius of 16. What steps will help show that circle A is similar to circle B?

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.

Step-by-step 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 ():

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.

594 square inches

step-by-step explanation:

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