Circle A has a radius of $3$ $3$ and a center of $(5, 4)$ $(5 ,4 )$ . Circle B has a radius of $4$ $4$ and a center of $(7, 2)$ $(7 ,2 )$ . If circle B is translated by $< 3, 2 >$ $<3 ,2 >$ , does it overlap circle A? If not, what is the minimum distance between points on both circles?

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Answer 1 · 2017-07-06T14:08:38

The circles overlap

Let the center of the circle $A$ $A$ be $O_{A} = (5, 4)$ $O_A=(5,4)$

and the center of the circle $B$ $B$ be $O_{B} = (7, 2)$ $O_B=(7,2)$

The center after translation is

$O_B'=(7,2)+ <3,2> =(10,4)$

The distance between the centers is

$O_AO_B'=sqrt((10-5)^2+(4-4)^2)$

$=5$

The sum of the radii is

$r_A+r_B=3+4=7$

As ,

$O_AO_B'<(r_A+r_B)$

The circles overlap

graph{((x-5)^2+(y-4)^2-9)((x-7)^2+(y-2)^2-16)((x-10)^2+(y-4)^2-16)=0 [-6, 16.5, -2.185, 9.065]}

Circle A has a radius of 3 33 and a center of (5 ,4 )(5,4)(5 ,4 ). Circle B has a radius of 4 44 and a center of (7 ,2 )(7,2)(7 ,2 ). If circle B is translated by <3 ,2 ><3,2><3 ,2 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?