Question

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

Answer 1

`"circle B inside circle A"`

Explanation:

`"What we have to do here is compare the distance (d)"`
`"to the sum/difference of radii"`

`• " if sum of radii">d" then circles overlap"`

`• " if sum of radii"< d" then no overlap"`

`• " if difference of radii"> d" one circle inside other"`

`"Before calculating d we require to find the new centre"`
`"of B under the given translation"`

`"under the translation "< 2,-1>`

`(1,4)to(1+2,4-1)to(3,3)larrcolor(red)"new centre of B"`

`"calculate d using the "color(blue)"distance formula"`

`•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)`

`"let "(x_1,y_1)=(3,3)" and "(x_2,y_2)=(3,2)`

`d=sqrt((3-3)^2+(3-2)^2)=sqrt1=1`

`"sum of radii "=5+2=7`

`"difference of radii "=5-2=3`

`"since difference of radii">d" circle B inside circle A"`
graph{((x-3)^2+(y-2)^2-25)((x-3)^2+(y-3)^2-4)=0 [-40, 40, -20, 20]}