Two circles have the following equations (x +5 )^2+(y +3 )^2= 9 and (x +4 )^2+(y -1 )^2= 1 . 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?

1 Answer
CW
Sep 24, 2016

No overlap of the circles. Greatest distance =8.123

Explanation:

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Circle A, center (-5,-3), r_A=3
Circle B, center (-4,1), r_B=1

Now compare the distance d between the centres of the circles to the sum of the radii.

1) If the sum of the radii >d, the circles overlap.
2) If the sum of the radii <d, then no overlap.
3)If the difference of the radii >d, then one circle inside the other.

To calculate d, use the distance formula :
d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)

where (x_1,y_1) and (x_2,y_2) are 2 coordinate points

here the two points are (-5,-3) and (-4,1) the centres of the circles

let(x_1,y_1)=(-5,-3) and (x_2,y_2)=(-4,1)

d=sqrt((-4-(-5))^2+(1-(-3))^2)=sqrt(1^2+(4)^2)=sqrt17=4.123

Sum of radii = radius of A + radius of B = 3+1=4

Since sum of radius <d, then no overlap of the circles

greatest distance :
d+sum of radii = 4.123+3+1 =8.123

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