Circles: Similarity and Construction

True or False

All circles are similar.

• True

• False

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

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.

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

In order to construct the inscribed circle of a triangle, you have to construct ______(?)_________.

• the orthocenter

• the circumcenter

• the incenter

• the centroid

The steps to construct a circumscribed circle of a triangle includes which of the following?

• Construct perpendicular bisectors of 2 sides of the triangle.

• Construct the incenter.

• Construct angle bisectors of all angles.

• Construct the centroid.

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.

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.

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.

Which of the following is the last 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.