# Circle A has a radius of #5 # and a center of #(8 ,2 )#. Circle B has a radius of #3 # and a center of #(3 ,7 )#. If circle B is translated by #<4 , 8 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

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To determine if circle B overlaps circle A after being translated, we need to find the distance between the centers of the circles after the translation and compare it to the sum of the radii of the circles.

The center of circle B after translation is obtained by adding the translation vector to the original center coordinates of circle B:

New center of circle B = (3 + 4, 7 + 8) = (7, 15)

Now, we calculate the distance between the centers of the circles:

Distance between centers = √[(x2 - x1)^2 + (y2 - y1)^2] = √[(7 - 8)^2 + (15 - 2)^2] = √[(-1)^2 + (13)^2] = √(1 + 169) = √170

Now, we compare this distance to the sum of the radii of the circles:

Sum of radii = 5 + 3 = 8

Since the distance between the centers (sqrt(170)) is greater than the sum of the radii (8), the circles do not overlap.

To find the minimum distance between points on both circles, we subtract the radii of the circles from the distance between their centers:

Minimum distance = Distance between centers - Sum of radii = √170 - 8 = √170 - 8 ≈ 3.96 units

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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.

- Please answer my question. It is optional maths?
- Circle A has a radius of #3 # and a center of #(3 ,2 )#. Circle B has a radius of #5 # and a center of #(1 ,7 )#. If circle B is translated by #<2 ,-1 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
- Circle A has a radius of #4 # and a center of #(7 ,3 )#. Circle B has a radius of #2 # and a center of #(1 ,2 )#. If circle B is translated by #<2 ,4 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
- Points A and B are at #(4 ,1 )# and #(3 ,7 )#, respectively. Point A is rotated counterclockwise about the origin by #pi # and dilated about point C by a factor of #3 #. If point A is now at point B, what are the coordinates of point C?
- Point A is at #(-5 ,9 )# and point B is at #(-1 ,7 )#. Point A is rotated #(3pi)/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?

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