Circle A has a radius of $5$ $5$ and a center of $(8, 2)$ $(8 ,2 )$ . Circle B has a radius of $3$ $3$ and a center of $(3, 7)$ $(3 ,7 )$ . If circle B is translated by $< 2, - 1 >$ $<2 ,-1 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Answer 1 · 2016-09-30T20:02:20

The distance between the two centers is equal to the radius of the larger circle, therefore, the circles overlap

The new center of circle B is (5, 6)

The distance between the two centers is:

$d = \sqrt{{(8 - 5)}^{2} + {(2 - 6)}^{2}}$ $d = sqrt((8 - 5)^2 + (2 - 6)^2)$

$d = \sqrt{3^{2} + {(- 4)}^{2}}$ $d = sqrt(3^2 + (-4)^2)$

$d = \sqrt{9 + 16}$ $d = sqrt(9 + 16)$

$d = 5$ $d = 5$

The distance between the two centers is equal to the radius of the larger circle, therefore, the circles overlap

Circle A has a radius of 55 and a center of (8,2)(8 ,2 ). Circle B has a radius of 33 and a center of (3,7)(3 ,7 ). If circle B is translated by <2,−1><2 ,-1 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?