# Circle A has a center at #(5 ,1 )# and an area of #4 pi#. Circle B has a center at #(2 ,8 )# and an area of #16 pi#. Do the circles overlap? If not, what is the shortest distance between them?

They do not overlap. The closest distance is

The radius of circle A is: 2

The radius of circle B is: 4

The distance, d, between the centers is:

This is greater than the sum of the radii, thefore, the circles do not overlap.

Here is a graph of the two circles:

The closest distance is

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Yes, the circles overlap. The shortest distance between their centers is the distance between the points (5, 1) and (2, 8), which can be found using the distance formula. The distance between these points is approximately 7.62 units. Since the sum of the radii of the circles (which is the distance between their centers) is less than the distance between the centers, 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.

- Circle A has a center at #(8 ,3 )# and a radius of #1 #. Circle B has a center at #(4 ,4 )# and a radius of #2 #. Do the circles overlap? If not what is the smallest distance between them?
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- What is the Endpoint Formula?
- A line passes through #(4 ,7 )# and #(6 ,4 )#. A second line passes through #(3 ,5 )#. What is one other point that the second line may pass through if it is parallel to the first line?

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