Question

Circle A has a radius of `2` and a center of `(5 ,7 )`. Circle B has a radius of `4` and a center of `(3 ,8 )`. 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 are concentric

Explanation:

A translation does not change the shape of a figure , only it's position.

Under a translation of `((2),(-1))`

centre of B (3 , 8) → (3 + 2 , 8 - 1) → ( 5 , 7)

This means that circle B now has the same centre as A

Hence the circles are concentric. Circles have same centre but different radii.

They , therefore do not overlap and the distance between them is the difference in their radii . That is 4 - 2 = 2.

Here is what concentric circles look like.
graph{(y^2-10y+x^2-16x+85)(x^2+y^2-10y-16x+73)=0 [-20, 20, -10, 10]}