# Circle A has a radius of 4  and a center of (6 ,1 ). Circle B has a radius of 1  and a center of (5 ,3 ). If circle B is translated by <-2 ,2 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Apr 11, 2016

circles have a single point of contact.

#### Explanation:

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

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

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

Now 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 $\left({x}_{1} , {y}_{1}\right) = \left(6 , 1\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(3 , 5\right)$

d $= \sqrt{{\left(3 - 6\right)}^{2} + {\left(5 - 1\right)}^{2}} = \sqrt{9 + 16} = \sqrt{25} = 5$

now: radius of A + radius of B = 4 + 1 = 5

Since sum of radii = distance between centres , then the circles will have a single point of contact.