# Circle A has a radius of 2  and a center of (6 ,2 ). Circle B has a radius of 3  and a center of (5 ,7 ). If circle B is translated by <-1 ,2 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Apr 9, 2016

no overlap , d ≈ 2.28

#### Explanation:

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

Under a translation of $\left(\begin{matrix}- 1 \\ 2\end{matrix}\right)$

Centre of B (5 , 7) → (5-1 , 7 + 2 ) → (4 , 9)

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 $\left({x}_{1} , {y}_{1}\right) = \left(6 , 2\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(4 , 9\right)$

d = sqrt((4-6)^2 + (9-2)^2) = sqrt(4 + 49) = sqrt53 ≈ 7.28

now, radius of A + radius of B = 2 + 3 = 5

Since sum of radii < distance between centres , no overlap

and distance between circles (d) = 7.28 - 5 = 2.28