What is the locus of all points in the plane that are no more than 8 inches from point Q?

Question

1. A circle with radius 8 inches and all points outside the circle 

2. A circle with radius 8 inches and all points inside the circle

3. A circle with radius 16 inches and all points outside the circle

4. A circle with radius 16 inches and all points inside the circle 

Answer 1

You must learn to try things--in Geometry, this means make a sketch. Begin with point Q near center of paper.

Find one point A that is 8" away; find others that are 8" away from Q, in various other directions from Q.

Now find another point along QA, but less than 8" from Q. Do a similar thing for other points, in other directions.

Now use your imagination to characterize ALL possible points not more than 8" away from Q, in ANY direction.

Describe this locus! DONE.