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Circle A has a center at #(3 ,2 )# and a radius of #2 #. Circle B has a center at #(1 ,3 )# and a radius of #4 #. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

Sadie Allen

circles overlap

First step is to find the distance between the centres using the#color(blue)" distance formula " #

#d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2 #

where#(x_1,y_1)" and " (x_2,y_2)" are the coords of 2 points "#

let#(x_1,y_1)=(3,2)" and " (x_2,y_2)=(1,3) #

#d = sqrt((1-3)^2 + (3-2)^2) = sqrt(4+1) = sqrt5 ≈ 2.236 #

radius of A + radius of B = 2 + 4 = 6

since 6 > 2.236 , circles will overlap

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Answer 2

Sophia Alfred

Yes, the circles overlap. The smallest distance between the circles is 0 units.

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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.