# Circle A has a radius of 2  and a center of (1 ,7 ). Circle B has a radius of 6  and a center of (8 ,1 ). If circle B is translated by <-4 ,3 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Feb 9, 2018

Circles Overlap

#### Explanation:

Given :
${O}_{A} \left(\begin{matrix}1 \\ 7\end{matrix}\right) , {R}_{A} = m 2 , {O}_{B} \left(\begin{matrix}8 \\ 1\end{matrix}\right) , {R}_{B} = 6$

Circle B translated by $\left(\begin{matrix}- 4 \\ 3\end{matrix}\right)$

Sum of Radii R_A + R_B = 2 + 6 = color(purple)(8

New coordinates of ${O}_{B} \to \left(\begin{matrix}8 - 4 \\ 1 + 3\end{matrix}\right) \implies \left(\begin{matrix}4 \\ 4\end{matrix}\right)$

vec(O_AO_B) = sqrt((4-1)^2 + (4-7)^2) = sqrt18 ~~ color(green)(4.24

Since sum of radii greater than the distance between the two circle

centers, Circles Overlap

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