Two circles have the following equations: $(x +2 )^2+(y -1 )^2= 49$ and $(x +4 )^2+(y +7 )^2= 25$ . Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?

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Answer 1 · 2017-08-11T18:17:08

The circles overlap and the greatest distance is $=20.25$

The radius of the circles are

$r_A=7$

$r_B=5$

The sum of the radii is

$r_A+r_B=7+5=12$

The centers of the circles are $(-2,1)$ and $(-4,-7)$

The distance between the centers is

$d=sqrt((-4-(-2))^2+(-7-(1))^2)$

$=sqrt((-2)^2+(-8)^2)$

$sqrt(4+64)=sqrt68=8.25$

As,

$(r_A+r_B) >d$ , the circles overlap

The greatest distance is

$=d+r_A+r_B=12+8.25=20.25$

Two circles have the following equations: (x +2 )^2+(y -1 )^2= 49 (x +2 )^2+(y -1 )^2= 49 and (x +4 )^2+(y +7 )^2= 25 (x +4 )^2+(y +7 )^2= 25 . Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?