Circle A has a radius of 4  and a center of (7 ,3 ). Circle B has a radius of 2  and a center of (1 ,2 ). If circle B is translated by <2 ,3 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Apr 27, 2016

circles overlap

Explanation:

What we have to do here is calculate the distance (d) between the centres of A and B and compare this with the sum of the radii.

• If sum of radii > d , then circles overlap

• If sum of radii < d , then no overlap

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

centre of B(1 ,2) → (1+2 , 2+3) → (3 ,5)

Calculate d 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 $\left({x}_{1} , {y}_{1}\right) \text{ and " (x_2,y_2)" are 2 points }$

let $\left({x}_{1} , {y}_{1}\right) = \left(7 , 3\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(3 , 5\right)$

d=sqrt((3-7)^2+(5-3)^2)=sqrt(16+4)=sqrt20 ≈ 4.472

radius of A + radius of B = 4 + 2 = 6

Since sum of radii > d , circles overlap