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

Apr 6, 2016

no overlap , d ≈ 2.81

Explanation:

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

Under a translation of $\left(\begin{matrix}- 3 \\ 2\end{matrix}\right)$

centre B (4,5) → (4-3 , 5+2) → (1 , 7)

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 $\left({x}_{1} , {y}_{1}\right) = \left(6 , 1\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(1 , 7\right)$

d =sqrt((1-6)^2 + (7-1)^2) = sqrt(25+36) = sqrt61 ≈ 7.81

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

since sum of radii < distance between centres , no overlap.

and distance between them = 7.81 - 5 = 2.81