# Circle A has a radius of 3  and a center of (2 ,7 ). Circle B has a radius of 4  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?

Feb 9, 2018

Circles overlap .

Minimum distance between the circles is

#### Explanation:

Given : $A \left(2 , 7\right) , {R}_{A} = 3$, $B \left(7 , 5\right) , {R}_{B} = 4$ B translated by (-1, 1)

Therefore, new coordinates of $B \left(\begin{matrix}7 - 1 \\ 5 + 1\end{matrix}\right) = B \left(\begin{matrix}6 \\ 6\end{matrix}\right)$

Distance between A and new B

$d = \sqrt{{\left(2 - 6\right)}^{2} + {\left(7 - 6\right)}^{2}} = \sqrt{17} \approx 4.123$

Circles overlap if$d < {R}_{A} + {R}_{B}$ and NOT if $d > {R}_{a} + {R}_{B}$

${R}_{A} + {R}_{B} = 3 + 4 = 7$

Since $d < {R}_{A} + {R}_{B}$, circles overlap