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

Apr 14, 2016

no overlap , d ≈ 3.32

#### Explanation:

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

Under a translation of $\left(\begin{matrix}- 2 \\ 5\end{matrix}\right)$

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

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

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where $\left({x}_{1} , {y}_{1}\right) \text{ and " (x_2,y_2)" are 2 coordinate points }$

let $\left({x}_{1} , {y}_{1}\right) = \left(1 , 2\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(3 , 8\right)$

d = sqrt((3-1)^2 + (8-2)^2)=sqrt(4+36)=sqrt40 ≈ 6.32