Circle A has a radius of $3$ $3$ and a center of $(8, 7)$ $(8 ,7 )$ . Circle B has a radius of $2$ $2$ and a center of $(6, 1)$ $(6 ,1 )$ . If circle B is translated by $< 2, 7 >$ $<2 ,7 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Answer 1 · 2018-02-09T11:47:07

Circles Overlap

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Given : $O_A ((8),(7)), R_A = 3, O_B ((6),(1)), R_B = 2$

$O_B$ translated by $(2,7)$

New $O_B -> ((6+2),(1+7)) => ((8),(8))$

$vec(O_AO_B) = sqrt((8-8)^2 + (8-7)^2) = 1$

Sum of Radii $R_A + R_B = 3 + 2 = 5$

Since #R_A + R_B > vec(O_AO_B), both the circles overlap

Circle A has a radius of 3 33 and a center of (8 ,7 )(8,7)(8 ,7 ). Circle B has a radius of 2 22 and a center of (6 ,1 )(6,1)(6 ,1 ). If circle B is translated by <2 ,7 ><2,7><2 ,7 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?