Circle A has a center at #(7 ,-5 )# and a radius of #1 #. Circle B has a center at #(4 ,2 )# and a radius of #4 #. Do the circles overlap? If not, what is the smallest distance between them?
1 Answer
Feb 2, 2016
The circles don't overlap, and the smallest distance between them = 2.62
Explanation:
- First: using the formula :
#d=sqrt((x_1-x_2)^2+(y_1-y_2)^2)#
the distance between the two centers
-
Second:
The distance between the two centers > the sum of the two radii.
Meaning the circles don't overlap. -
Third: The smallest distance between them is the portion of the line connecting the two centers that doesn't fall in either circle. Or
#s# in the image below.