Question

Circle A has a radius of `2` and a center of `(2 ,7 )`. Circle B has a radius of `6` 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?

Answer 1

circle B do not overlap.
Shortest distance is `3.764-2=1.764`

Explanation:

Circle A
Center `(2,7)`
radius `2`

Equation of circle A
`(x-2)^2+(y-7)^2=2^2`

Circle B
Center `(7,5)`
radius `6`

Equation of circle B
`(x-7)^2+(y-5)^2=6^2`

ranslation of B
<-1,1>
Center of B after translation `((7-1),(5+1))`
Center of B after translation `(6,6)`

Equation of circle B after translation
`(x-6)^2+(y-6)^2=6^2`

Intersection of the circles
`(x-2)^2+(y-7)^2=2^2`
and
`(x-6)^2+(y-6)^2=6^2`
can be found out

Distance from center of Circle A to
center of Circle B is
`(2,7) ---- (6,6)`
`=sqrt((6-7)^2+(6-2)^2`
`=sqrt((1+4)`
`=sqrt(5)`
`=2.236`

Radius of circle A is `2`
point on the Perimeter of the circle B is away from its center by 6
point on the Perimeter of the circle B is away from (2,7) is`6-2.236`
`=3.764`
Hence, the two circles donot overlap.
Shortest distance is `3.764-2=1.764`