Two circles have the following equations (x +5 )^2+(y +6 )^2= 36 and (x +2 )^2+(y -1 )^2= 81 . 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
Shwetank Mauria
Apr 9, 2016

Smaller circle is not contained in larger circle and they intersect each other. The greatest possible distance between a point on one circle and another point on the other will be 22.6158.

Explanation:

First circle has center as (-5,-6) and radius 6 and second circle has center as (-2,1) and radius 9.

Distance between circles of two centers is sqrt((-2-(-5))^2+(1-(-6))^2 or sqrt(3^2+7^2)=sqrt(9+49)=sqrt58=7.6158

As the distance between two circles at 7.6158 is less than the sum of their radii 6+9=15 and more than the difference between them at 9-63, smaller circle is not contained in larger circle and they intersect each other.

The greatest possible distance between a point on one circle and another point on the other will be 6+9+7.6158=22.6158.

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