Circle A has a center at #(-2 ,-1 )# and a radius of #3 #. Circle B has a center at #(1 ,3 )# and a radius of #2 #. Do the circles overlap? If not what is the smallest distance between them?

Answer 1

Noah Atkinson

The circles touch one another without overlapping.

The distance between the centers is

#d=sqrt((-2-1)^2+(-1-3)^2)#

#=sqrt(9+16)#

#=sqrt25=5#

The sum of the radii is

#r_A+r_B=3+2=5#

#d=r_A+r_B#

graph{((x+2)^2+(y+1)^2-9)((x-1)^2+(y-3)^2-4)=0 [-7.23, 5.26, -2.293, 3.947]}

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Answer 2

Savannah Aguilar

Yes, the circles overlap. The distance between the centers of the circles is greater than the sum of their radii. The distance between the centers of Circle A and Circle B is approximately 7.07 units, which is greater than the sum of their radii (3 + 2 = 5 units). Therefore, the circles overlap.

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Answer from HIX Tutor

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.