Two circles have the following equations #(x -1 )^2+(y -7 )^2= 25 # and #(x +3 )^2+(y +3 )^2= 49 #. 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
Dec 1, 2016
The farthest possible distance between two points, one on each circle, is the sum of the two radii and the distance between the centers:
Explanation:
The first circle has a center at
The second circle has a center at
The distance, d, between their centers is:
The circle partially overlap but the larger does not contain the smaller. Please see the drawing:
The farthest possible distance between two points, one on each circle, is the sum of the two radii and the distance between the centers:
