Question

Circle A has a radius of `3` and a center of `(8 ,5 )`. Circle B has a radius of `2` and a center of `(6 ,1 )`. If circle B is translated by `<2 ,7 >`, 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 the radii"`

• If sum of radii > d , then circles overlap

• If sum of radii < d , then no overlap

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

Under a translation of `((2),(7))`

`(6,1)to(6+2,1+7)to(8,8)larr" new centre of B "`

To calculate d, in this case since the coordinates of the centres (8 ,5) and (8 ,8) have the same x-coordinate- that is they lie on the same vertical line, then d is the difference in the y-coordinates.

`rArrd=8-5=3`

Sum of radii = radius of A + radius of B = 3 + 2 + 5

Since sum of radii > d , then the circles overlap
graph{(y^2-10y+x^2-16x+80)(y^2-16y+x^2-16x+124)=0 [-28.48, 28.48, -14.22, 14.26]}