Two points C and D are located 12 feet apart. How many points are 6 feet from point C and 4 feet from point D?
To find the number of points that are 6 feet from point C and 4 feet from point D, we can use geometrical reasoning.
Imagine a line segment connecting points C and D. This line segment represents the 12-foot distance between points C and D. Let's call this line segment CD.
Now, let's draw two circles centered at points C and D with radii of 6 feet and 4 feet, respectively. The circle centered at point C represents the set of all points that are 6 feet from point C, and the circle centered at point D represents the set of all points that are 4 feet from point D.
Since we are looking for points that are 6 feet from point C and 4 feet from point D, we need to find the common points of intersection between these two circles. These common points will be the points that satisfy the given condition.
To determine the number of common points, we need to consider the geometric possibilities. There are three scenarios:
1. The circles do not intersect at all: In this case, there are no points that satisfy the given condition. The number of common points is 0.
2. The circles intersect tangentially: In this case, the circles touch at a single point. The number of common points is 1.
3. The circles intersect at two distinct points: In this case, there are two common points.
Therefore, depending on the geometric scenario, the number of points that are 6 feet from point C and 4 feet from point D can be either 0, 1, or 2.
To determine the specific scenario, we need additional information about the relative positions of points C and D.