Circle A has a radius of $1$ $1$ and a center at $(2, 3)$ $(2 ,3 )$ . Circle B has a radius of $3$ $3$ and a center at $(6, 4)$ $(6 ,4 )$ . If circle B is translated by $< - 3, 4 >$ $<-3 ,4 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Answer 1 · 2018-02-09T10:12:05

Since $R_{A} + R_{B} < - --- \to O_{A} O_{B}$ $R_A + R_B < vec(O_AO_B)$ , circles do NOT overlap

Minimum distance between the two circles A & B is $5.1 - 4 = 1.1$ $5.1 - 4 = color(red)(1.1$

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Given : $O_{A} (2, 3), R_{A} = 1, O_{B} (6, 4), R_{B} = 3$ $O_A (2,3), R_A = 1, O_B (6,4), R_B = 3$

$O_{B}$ $O_B$ translated by (-3,4)

New coordinates of $O_B ((6-3),(4+4)) => ((3),(8))$

Now, $vec(O_AO_B) = sqrt((2-3)^2 + (3-8)^2) = sqrt26 ~~ 5.1$

Sum of radii $R_A + R_B = 1 + 3 = 4$

Since $R_A + R_B < vec(O_AO_B)$ , circles do NOT overlap

Minimum distance between the two circles A & B is $5.1 - 4 = 1.1$

Circle A has a radius of 1 11 and a center at (2 ,3 )(2,3)(2 ,3 ). Circle B has a radius of 3 33 and a center at (6 ,4 )(6,4)(6 ,4 ). If circle B is translated by <-3 ,4 ><−3,4><-3 ,4 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?