Describe the conditions necessary for the two circles, where circle a has a larger radius than circle b, to have no points of intersection, while each circle is entirely in the exterior of the other circle.
To determine the conditions necessary for two circles, where circle A has a larger radius than circle B, to have no points of intersection and each circle to be entirely in the exterior of the other circle, we need to consider their relative positions.
First, let's assume that circle A is the larger circle with radius R_A, and circle B is the smaller circle with radius R_B.
For the circles to have no points of intersection, the distance between their centers must be greater than the sum of their radii. Mathematically, this can be expressed as:
Distance between centers (d) > R_A + R_B
If this condition is not met, the circles will intersect or overlap.
Now, let's consider the condition where both circles are entirely in the exterior of each other. In this case, the distance between their centers should be greater than the difference between their radii. Mathematically, this can be expressed as:
Distance between centers (d) > |R_A - R_B|
To summarize:
1. For no points of intersection:
Distance between centers (d) > R_A + R_B
2. For each circle to be entirely in the exterior of the other circle:
Distance between centers (d) > |R_A - R_B|
By checking these conditions, you can determine whether two circles with different radii will have no points of intersection and be entirely in the exterior of each other.