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Circle A has a center at #(8 ,1 )# and an area of #81 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?

Answer 1

Circle A and Circle do overlap.

Circle A, centered at (8,1), area #= pir^2=81pi => r=9#

Circle B, centered at (4,2), area #= pir^2=36pi => r=6#

distance between the two center points #=sqrt((2-1)^2+(4-8)^2)=sqrt17 =4.123#

As the distance between the two centers (4.123) is smaller than the sum of the two radii (9+6=15), the two circle overlaps.

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Answer 2

Ella Armstrong

Yes, the circles overlap. The shortest distance between their centers is the distance between the points (8, 1) and (4, 2), which can be calculated using the distance formula:

Distance = √[(x2 - x1)^2 + (y2 - y1)^2] = √[(4 - 8)^2 + (2 - 1)^2] = √[(-4)^2 + (1)^2] = √[16 + 1] = √17

Therefore, the shortest distance between the centers of the circles is √17.

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Answer from HIX Tutor

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