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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?

Answer 1

Autumn Armstrong

They do not overlap. The closest distance is #d = sqrt(58) - 6 ~~ 1.6#

The radius of circle A is: 2
The radius of circle B is: 4

The distance, d, between the centers is:

#d = sqrt((5 - 2)^2 + (1 - 8)^2)#

#d = sqrt((3)^2 + (-7)^2)#

#d = sqrt(58)#

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 #d = sqrt(58) - 6 ~~ 1.6#

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Answer 2

Caroline Aucoin

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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Answer from HIX Tutor

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