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

Question

1319 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-21T06:16:50

The circles do not overlap. The minimum distance is $= 1.3$ $=1.3$

The sum of the radii of the circles is

$r_{A} + r_{B} = 1 + 4 = 5$ $r_A+r_B=1+4=5$

The center of circle $B$ $B$ after translation is

$= (5, 3) + < - 2, 5 \geq (3, 8)$ $=(5,3)+<-2,5>=(3,8)$

The distance between the centers is

$d = \sqrt{{(3 - 1)}^{2} + {(8 - 2)}^{2}} = \sqrt{4 + 36} = \sqrt{40} = 6.3$ $d=sqrt((3-1)^2+(8-2)^2)=sqrt(4+36)=sqrt40=6.3$

As

$d > r_{A} + r_{B}$ $d>r_A+r_B$

The circles do not overlap.

The minimum distance is

$= d - (r_{A} + r_{B}) = 6.3 - 5 = 1.3$ $=d-(r_A+r_B)=6.3-5=1.3$

graph{((x-1)^2+(y-2)^2-1)((x-3)^2+(y-8)^2-16)=0 [-12.58, 15.9, -3, 11.24]}

Circle A has a radius of 1 11 and a center of (1 ,2 )(1,2)(1 ,2 ). Circle B has a radius of 4 44 and a center of (5 ,3 )(5,3)(5 ,3 ). If circle B is translated by <-2 ,5 ><−2,5><-2 ,5 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?