# Circle A has a center at #(5 ,-2 )# and a radius of #2 #. Circle B has a center at #(4 ,6 )# and a radius of #4 #. Do the circles overlap? If not what is the smallest distance between them?

no overlap , d ≈ 2.062

radius of A + radius of B = 2 + 4 = 6

since sum of radii < distance between centres , no overlap

and distance between A and B ≈ 8.062 - 6 ≈ 2.062

By signing up, you agree to our Terms of Service and Privacy Policy

The distance between the centers of Circle A and Circle B can be found using the distance formula. If this distance is less than the sum of the radii of both circles, then the circles overlap. Otherwise, they do not overlap, and the smallest distance between them is the difference between the distance between their centers and the sum of their radii.

Distance between the centers of Circle A and Circle B: √((x₂ - x₁)² + (y₂ - y₁)²)

For Circle A (x₁, y₁) = (5, -2) For Circle B (x₂, y₂) = (4, 6)

Distance = √((4 - 5)² + (6 - (-2))²) = √(1² + 8²) = √(1 + 64) = √65 ≈ 8.06

Sum of the radii of both circles: Radius of Circle A = 2 Radius of Circle B = 4

Sum = 2 + 4 = 6

Since the distance between the centers of the circles (8.06) is greater than the sum of their radii (6), the circles do not overlap.

The smallest distance between the circles is the difference between the distance between their centers and the sum of their radii: Smallest distance = Distance - Sum = 8.06 - 6 ≈ 2.06 units

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- A triangle has corners at #(6 ,2 )#, #(4 ,3 )#, and #(5 ,1 )#. How far is the triangle's centroid from the origin?
- From a point #A# directly above (i.e. north of) point #B# in a map, a point #C# to the east of #B# is #6# miles. If #B# and #C# are #2# miles apart, what is the distant between #A# and #B#?
- What is the perimeter of a triangle with corners at #(7 ,9 )#, #(8, 2 )#, and #(9 ,4 )#?
- What is the perimeter of a triangle with corners at #(3 ,0 )#, #(5 ,2 )#, and #(5 ,4 )#?
- A triangle has corners at #(1 ,1 )#, #(8 ,2 )#, and #(5 ,9 )#. How far is the triangle's centroid from the origin?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7