Circle A has a radius of $3$ and a center of $(2 ,7 )$ . Circle B has a radius of $4$ and a center of $(7 ,5 )$ . If circle B is translated by $<-1 ,1 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Answer 1 · 2018-02-09T09:53:41

Circles overlap .

Minimum distance between the circles is

Given : $A(2,7), R_A = 3$ , $B (7,5), R_B = 4$ B translated by (-1, 1)

Therefore, new coordinates of $B( (7-1), (5+1)) = B((6),(6))$

Distance between A and new B

$d = sqrt((2-6)^2 + (7-6)^2) = sqrt17 ~~ 4.123$

Circles overlap if $d < R_A + R_B$ and NOT if $d> R_a + R_B$

$R_A + R_B = 3 + 4 = 7$

Since $d < R_A + R_B$ , circles overlap

Circle A has a radius of 3 3 and a center of (2 ,7 )(2 ,7 ). Circle B has a radius of 4 4 and a center of (7 ,5 )(7 ,5 ). If circle B is translated by <-1 ,1 ><-1 ,1 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?