# Circle A has a center at #(1 ,-2 )# and a radius of #3 #. Circle B has a center at #(-2 ,6 )# and a radius of #2 #. Do the circles overlap? If not, what is the smallest distance between them?

Let

Let

Then if:

We find the distance between centres using the distance formula:

We have:

Radius of

Radius of

Sum of radii:

The circles do not touch.

The shortest distance between the circles is:

See diagram:

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Yes, the circles overlap. The distance between the centers of the circles can be calculated using the distance formula, which is √((x2 - x1)^2 + (y2 - y1)^2). For these circles, the distance between their centers is approximately 9.2195 units. Since this distance is less than the sum of the radii (3 + 2 = 5), the circles overlap.

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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.

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- Circle A has a center at #(-2 ,-1 )# and a radius of #3 #. Circle B has a center at #(1 ,3 )# and a radius of #2 #. Do the circles overlap? If not what is the smallest distance between them?
- Circle A has a center at #(5 ,-2 )# and a radius of #6 #. Circle B has a center at #(-4 ,-8 )# and a radius of #5 #. Do the circles overlap? If not, what is the smallest distance between them?

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