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

Apr 5, 2016

circles overlap.

#### Explanation:

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

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

centre of B (7,5) → (7-1 , 5+1) → (6,6)

We now require to calculate the distance between the 2 centres 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 $\left({x}_{1} , {y}_{1}\right) = \left(2 , 7\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(6 , 6\right)$

d =sqrt((6-2)^2+(6-7)^2) = sqrt(16+1) = sqrt17 ≈ 4.123

radius of A + radius of B = 3 + 6 = 9

Since sum of radii > distance between centres, circles overlap.