# Circle A has a radius of 2  and a center of (8 ,2 ). Circle B has a radius of 4  and a center of (2 ,3 ). If circle B is translated by <-1 ,5 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Apr 6, 2016

no overlap , d ≈ 3.22

#### Explanation:

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

Under a translation of $\left(\begin{matrix}- 1 \\ 5\end{matrix}\right)$

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

We now require to calculate the distance between the centres of A and B using the $\textcolor{b l u e}{\text{ distance formula }}$

$d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$

where $\left({x}_{1} , {y}_{1}\right) \text{ and " (x_2,y_2)" are 2 coordinate points }$

let $\left({x}_{1} , {y}_{1}\right) = \left(8 , 2\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(1 , 8\right)$

 d = sqrt((1-8)^2 + (8-2)^2) = sqrt(49+36) = sqrt85 ≈ 9.22

now: radius of A + radius of B = 2 + 4 = 6

since sum of radii < distance between centres , no overlap

and distance between them = 9.22 - 6 = 3.22