Circle A has a radius of $4$ $4$ and a center of $(7, 3)$ $(7 ,3 )$ . Circle B has a radius of $2$ $2$ and a center of $(2, 2)$ $(2 ,2 )$ . If circle B is translated by $< 1, 3 >$ $<1 ,3 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Answer 1 · 2018-02-09T11:54:09

circles overlap

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$O_A ((7),(3)), R_A = 4, O_B ((2),(2)), R_B = 2$

$O_B translated by ((1),(3))$

New coordinates of $O_B -> ((2+1),(2+3)) => ((3),(5))$

$vec(O_AO_B) = sqrt((7-3)^2 + (3-5)^2) = sqrt20 ~~ 4.47$

Sum of Radii $R_A + R_B = 4 + 2 = 6$

$R_A + R_B > vec(O_AO_B)$ and both the circles overlap

Circle A has a radius of 4 44 and a center of (7 ,3 )(7,3)(7 ,3 ). Circle B has a radius of 2 22 and a center of (2 ,2 )(2,2)(2 ,2 ). If circle B is translated by <1 ,3 ><1,3><1 ,3 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?