Question

Circle A has a radius of `4` and a center of `(5 ,3 )`. Circle B has a radius of `3` 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

`"circles overlap"`

Explanation:

What we have to do here is `color(blue)"compare"` the distance ( d) between the centres of the circles to the `color(blue)"sum of radii"`

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

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

Before calculating d we require to find the 'new ' centre of B under the given translation which does not change the shape of the circle only it's position.

`"under a translation "((2),(-1))`

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

`"since "(5,3)" and "(3,3)" have the same y-coordinate then"`
`"d is the difference of the x-coordinates"`

`rArrd=5-3=2`

`"sum of radii "=4+3=7`

`"since sum of radii ">d" then circles overlap"`
graph{((x-5)^2+(y-3)^2-16)((x-3)^2+(y-3)^2-9)=0 [-20, 20, -10, 10]}