Circle Similarity

What is the dilation scale factor for mapping circle B onto circle A?

• 9/16

• 4/3

• 3/4

• 1

All circles are similar.

• True

• False

The radius of one circle is 9mm and the radius of a second circle is 21mm. What is the ratio of their circumferences in simplest form?

• 9:21

• 1:3

• 3:7

• 9:49

The circumference of Circle A is 24π feet.

The circumference of Circle B is 4π feet.

What is the ratio of their radii in simplest form?

• 24:4

• 48:8

• 1:6

• 6:1

Circle A has center (2, 7) and radius 2. Circle B has center (9, 1) and radius 5. Which transformations can be used to show that the two circles are similar?

• Translate circle A right 7 and down 6 and then dilate with scale factor 5/2 and center (9, 1)

• Translate circle A left 7, up 6 and then dilate with scale factor 2/5 and center (9, 1).

• Dilate circle A using center (2, 7) and scale factor 2/5 then translate right 7 and down 6

• Reflect circle A over x = 5.5 and translate up 6 units.

The best way to demonstrate that all circles are similar is to show that

• they're all round

• they all have centers

• a combination of transformations can 'make' one circle become another

• since pi is 3.14, and pies are round and circular, then it's obvious

Circles X and Y have a similarity ratio of 1/2. Which of the following could NOT be true about the circles?

• Circle X has a radius of 5 while Circle Y has a radius of 10.

• Circle X has a circumference of 15π and Circle Y has a circumference of 30π.

• Circle X has a radius of 12 while Circle Y has a radius of 6.

• Circle X has a circumference of 60π while Circle Y has a circumference of 20π.

What is the translation vector for Circle B to Circle A?

• (x, y) →(x + 8, y - 4)

• (x, y) →(x - 4, y + 8 )

• (x, y) →(x - 8, y + 4)

• (x, y) →(x + 4, y - 8)

Circles X and Y have a similarity ratio of 1/2. Which of the following could NOT be true about the circles?

• Circle X has a radius of 5 while Circle Y has a radius of 10.

• Circle X has a circumference of 15π and Circle Y has a circumference of 30π.

• Circle X has a radius of 6 while Circle Y has a radius of 12.

• Circle X has a circumference of 60π while Circle Y has a circumference of 20π.

If the scale factor between two arcs is 5/6, then the ratio of areas is...

• 5:6

• 10:12

• 25:36

• 125:216