# Circle A has a center at #(8 ,5 )# and an area of #100 pi#. Circle B has a center at #(4 ,2 )# and an area of #36 pi#. Do the circles overlap? If not, what is the shortest distance between them?

circles overlap

What we have to do here is compare the distance ( d) between the centres of the circles to the sum of the radii.

• If sum of radii > d , then circles overlap

• If sum of radii < d , then no overlap

Before doing this we require to find the radii of the circles.

The 2 points here are (8 ,5) and (4 ,2) the centres of the circles.

sum of radii = radius of A + radius of B = 10 + 6 = 16

Since sum of radii > d , then circles overlap graph{(y^2-4y+x^2-8x-16)(y^2-10y+x^2-16x-11)=0 [-9.86, 9.88, -4.93, 4.935]}

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To determine whether the circles overlap, we need to calculate the distance between their centers and compare it to the sum of their radii.

The formula to calculate the distance between two points ((x_1, y_1)) and ((x_2, y_2)) in a two-dimensional plane is given by the distance formula:

[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} ]

Given the centers of Circle A at ((8, 5)) and Circle B at ((4, 2)), we can plug these values into the distance formula to find the distance between their centers.

Next, we compare this distance to the sum of the radii of the two circles. If the distance between the centers is greater than the sum of the radii, then the circles do not overlap.

If the distance between the centers is less than the sum of the radii, then the circles overlap.

To find the shortest distance between the circles if they do not overlap, we subtract the sum of the radii from the distance between their centers.

Let's perform these calculations.

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