Circles and Similarity

If Circle X is dilated by a scale factor of 3 to form Circle Y, which of the following statements is NOT true?

• The radius of Circle Y is 3 times the radius of Circle X.

• The diameter of Circle Y is 3 times the diameter of Circle X.

• The circumference of Circle Y is 3 times the circumference of Circle X.

• The area of Circle Y is 3 times the area of Circle X.

Tags

CCSS.7.G.A.1

Circle M is dilated by a scale factor of 3/2 and then translated along the vector <-1,3> to form circle M'. Which of the following is true?

• Circle M and circle M' are similar.

• Circle M and circle M' are congruent.

• Circle M and circle M' are concurrent.

• None of the above

Tags

CCSS.8.G.A.4

CCSS.HSG.SRT.A.2

All circles are similar.

• True

• False

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

If Circle A is dilated by a scale factor of 2 to form circle B, which of the following statements is true?

• The diameter of Circle A is equal to the diameter of Circle B.

• The area of Circle B is twice the area of Circle A.

• The ratio of the diameter to the circumference is the same for both circles.

• The radius of Circle A is twice the radius of Circle B

Tags

CCSS.8.G.A.3

Which of the following is the first step of constructing the tangent line from a point outside of circle C in the correct order.

• Place the compass on the midpoint of CX, adjust its length to reach the end point, and draw an arc across the circle.

• Construct the perpendicular bisector of segment CX.

• Draw a line connecting X to one of the points where the arc crosses the circle (tangent points)

• Draw a line segment connecting point X to the center of the circle.

Tags

CCSS.HSG.C.A.2

Which of the following is the second step of constructing the tangent line from a point outside of circle C in the correct order.

• Place the compass on the midpoint of CX, adjust its length to reach the end point, and draw an arc across the circle.

• Construct the perpendicular bisector of segment CX.

• Draw a line connecting X to one of the points where the arc crosses the circle (tangent points)

• Draw a line segment connecting point X to the center of the circle.

Tags

CCSS.HSG.C.B.5

Which of the following is the third step of constructing the tangent line from a point outside of circle C in the correct order.

• Place the compass on the midpoint of CX, adjust its length to reach the end point, and draw an arc across the circle.

• Construct the perpendicular bisector of segment CX.

• Draw a line connecting X to one of the points where the arc crosses the circle (tangent points)

• Draw a line segment connecting point X to the center of the circle.

Tags

CCSS.HSG.GPE.A.1

What is the translation vector of Circle B to Circle A.

• <-4, 1>

• <1, -4>

• <-1, 4>

• <4, -1>

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Two circles A and B have different radii.  A student dilates circle A at its center by a scale factor of 9/4 to make it the same size as circle B.  What scale factor could have been used to make circle B the same size as circle A?

• 3/2

• 2/3

• 4/9

• 9/4

Tags

CCSS.8.G.A.3

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

• <8, -4>

• <-4, 8>

• <-8, 4>

• <4, -8>

Tags

CCSS.HSG.CO.A.2