Circle A has a radius of $3$ $3$ and a center of $(5, 9)$ $(5 ,9 )$ . Circle B has a radius of $4$ $4$ and a center of $(1, 2)$ $(1 ,2 )$ . If circle B is translated by $< 3, - 1 >$ $<3 ,-1 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Answer 1 · 2018-02-09T12:15:31

circles do not overlap

Minimum distance between circles A & B is $8.06 - 7 = 1.06$ $8.06 - 7 = color(red)(1.06)$

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$R_A = 3, O_A ((5),(9)), R_B = 4, O_B ((1),(2))$ .

Center of circle B translated by $((3),(-1))$

Sum of radii $R_A + R_B = 3 + 4 = color(purple)(7)$

New coordinates of $O_B -> ((1+3),(2-1)) => ((4),(1))$

$vec(O_AO_B) = sqrt((5-4)^2 + (9-1)^2) = sqrt65 ~~ color(green)(8.06)$

$vec(O_AO_B) > R_A + R_B$

Hence the circles do not overlap

Minimum distance between circles A & B is $8.06 - 7 = color(red)(1.06)$

Circle A has a radius of 3 33 and a center of (5 ,9 )(5,9)(5 ,9 ). Circle B has a radius of 4 44 and a center of (1 ,2 )(1,2)(1 ,2 ). If circle B is translated by <3 ,-1 ><3,−1><3 ,-1 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?