# Circle A has a center at #(1 ,5 )# and an area of #18 pi#. Circle B has a center at #(8 ,4 )# and an area of #66 pi#. Do the circles overlap?

Get the distance between the centers. For the circles to overlap, the distance between the centers should be less than or equal to the sum of the radii but greater than or equal to the difference

Distance between centers:

The approximate distance between the centers is less than the sum of the radii but greater than the difference, the circles should overlap.

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

To determine if the circles overlap, we need to compare the distance between their centers to the sum of their radii. If the distance between the centers is less than the sum of their radii, the circles overlap.

First, we need to find the radii of both circles. We know that the area of a circle ((A)) is given by the formula (A = \pi r^2).

Given: For Circle A: (A = 18\pi) For Circle B: (A = 66\pi)

Using the formula for the area of a circle, we can find the radii of both circles:

For Circle A: [18\pi = \pi r_A^2] [r_A^2 = \frac{18\pi}{\pi}] [r_A^2 = 18] [r_A = \sqrt{18}]

For Circle B: [66\pi = \pi r_B^2] [r_B^2 = \frac{66\pi}{\pi}] [r_B^2 = 66] [r_B = \sqrt{66}]

Now, we find the distance between the centers of the circles using the distance formula:

Given: Center of Circle A: (1, 5) Center of Circle B: (8, 4)

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

[ d = \sqrt{(8 - 1)^2 + (4 - 5)^2} ] [ d = \sqrt{7^2 + (-1)^2} ] [ d = \sqrt{49 + 1} ] [ d = \sqrt{50} ]

Now, we compare the distance between the centers to the sum of the radii:

[ \text{Sum of radii} = r_A + r_B = \sqrt{18} + \sqrt{66} ]

If the distance between the centers ((\sqrt{50})) is less than the sum of the radii, the circles overlap.

If (\sqrt{50} < \sqrt{18} + \sqrt{66}), then the circles overlap.

If (\sqrt{50} < \sqrt{18} + \sqrt{66}), then the circles overlap.

Since (\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}), and (\sqrt{18} + \sqrt{66} > 5\sqrt{2}), the circles do not overlap.

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.

- Proof of the shortest distance from a point to a plane formula?
- Circle A has a center at #(1 ,2 )# and an area of #100 pi#. Circle B has a center at #(7 ,9 )# and an area of #36 pi#. Do the circles overlap? If not, what is the shortest distance between them?
- What is the perimeter of a triangle with corners at #(3 ,8)#, #(1 ,5 )#, and #(4 ,3 )#?
- A triangle has corners at #(1 ,3 )#, #(9 ,2 )#, and #(6 ,7 )#. How far is the triangle's centroid from the origin?
- Using the midpoint formula, if you're only given #((x_1 + x_2) / 2#, #(y_1 + y_2) / 2)#, is it possible to solve for #x# and #y#?

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