Question

A circle has radius 6 cm. In the plane of the circle what best describes the locus of points that are 2 cm from the circle.
Could you please tell me how you got your asnwer. Thank you!

Answer 1

@Directrix yay! finally someone! :)

Answer 2

Do you know the term "concentric circles?"

Answer 3

@Directrix no not really

Answer 4

Bear with me. Do you know how an archery target looks?

Answer 5

yes, so that is concentric?

Answer 6

Yes, circles in the same plane which have the same center but a different radius.

Answer 7

In the attached diagram, I have shown in red some points that are 2 cm from the given circle. If I drew ALL such points, what would the red points taken together form? That is half of the answer to your locus question.

Answer 8

@Directrix would I be correct in thinking the locus of points 2 cm away from the circle would be a circle of radius 8 cm?

Answer 9

Yes, you are. But, there is another "ring" of points in the plane of the given circle which are 2 cm from the given circle. Do you "see" them? If not, I'll start a diagram. Let me know. After that, we'll write the complete answer to the question.

Answer 10

@Directrix if it is like a target then the circles come in increments of 2 cm each?

Answer 11

They could. Look at the blue points that are 2 cm from the given circle in the attached diagram. If all such possible blue points were drawn, what would they form?

Answer 12

@Directrix is it best to describe the locus of points by saying a circle of radius 4 centimeters and a circle of radius 8 cm

Answer 13

Yes. The locus of points 2 cm from a given circle with radius 6 cm in a plane is two circles concentric to the given circle, one with radius 4 cm and the other with radius 8 cm.

Extra for Experts: Do you know what the locus would be for this problem if the points 2 cm away did NOT have to lie in the plane of the circle?

Answer 14

@Directrix a circle radius of 2? Could I ask you another question since you helped me a lot or should I wait my turn?

Answer 15

You have to think in 3-D so a circle radius of 2 is not correct.

What is the other question you have?

Answer 16

@Directrix Which description best fits the locus suggested by the figure?

Answer 17

I picked "all points equidistant from points A and B" but I could be wrong

Answer 18

@Directrix was I right or totally wrong :)

Answer 19

I see the photo but I do not see the descriptions.

If the diagram depicts the answer to some locus problem, I would agree with you but add a little more.

Question: What is the locus of points in the plane of points A and B and equidistant from points A and B?

By the way, the locus (a line) could be described as the perpendicular bisector of the segment determined by points A and B.

By the way, these same questions can be asked in 3-D and will yield different answers. I'm thinking you have not yet studied 3-D loci problems.

Answer 20

@Directrix I will give you a medal! :) here are the choices
A. all points 1 cm from line l
B. all points equidistant from points A and B
C. all points equidistant from line l
D. none of these

Answer 21

@blossombuttercupandbubbles1234

I agree with you: B. all points equidistant from points A and B

Answer 22

@Directrix Thank you so much! You're the best!

Answer 23

Glad to help. Geometry is fun.

Answer 24

@Directrix I know I'm asking a lot but can you help me with these other questions and then I swear I am done with asking questions! :)

Answer 25

Okay. Start a new thread. I'll follow you there.

Answer 26

Hey @Directrix :)