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

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

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Answer 1 · 2016-03-08T11:36:00

circles overlap

Explanation:

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

$d = \sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2}}$ $d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2$

where $(x_{1}, y_{1}) and (x_{2}, y_{2}) are the coords of 2 points$ $(x_1,y_1)" and " (x_2,y_2)" are the coords of 2 points "$

let $(x_{1}, y_{1}) = (3, 2) and (x_{2}, y_{2}) = (1, 3)$ $(x_1,y_1)=(3,2)" and " (x_2,y_2)=(1,3)$

$d = \sqrt{{(1 - 3)}^{2} + {(3 - 2)}^{2}} = \sqrt{4 + 1} = \sqrt{5} \approx 2.236$ $d = sqrt((1-3)^2 + (3-2)^2) = sqrt(4+1) = sqrt5 ≈ 2.236$

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

since 6 > 2.236 , circles will overlap

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

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Explanation:

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Circle A has a center at (3,2)(3 ,2 ) and a radius of 22 . Circle B has a center at (1,3)(1 ,3 ) and a radius of 44 . Do the circles overlap? If not, what is the smallest distance between them?

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