Circle A has a center at #(2 ,3 )# and a radius of #1 #. Circle B has a center at #(-1 ,-2 )# and a radius of #4 #. Do the circles overlap? If not, what is the smallest distance between them?

1 Answer
Oct 25, 2017

#therefore#Circles A and B do not intersect at all.

Explanation:

Two circles overlap if they intersect at two points .
#" "#
Two circle #A (O1,r1)" "and " " B (O2,r2)# intersect at two points
#" "#
#iff d(O1,O2) < r1+r2" "# where #" "d (O1,O2) # is the distance
#" "#
between the two centres.
#" "#
#d (O1,O2) = sqrt ((y_(O2)-y_(O1))^2 + (x_(O2)-X_(O1))^2)#
#" "#
#d (O1,O2) = sqrt((-2-3)^2+(-1-2)^2)#
#" "#
#d (O1,O2) = sqrt((-5)^2+(-3)^2)#
#" "#
#d (O1,O2) = sqrt(25+9)=sqrt34#
#" "#
Distance between the radii is:
#" "#
# r1+r2=1+4=5#
#" "#
#d (O1,O2)>r1+r2#
#" "#
#therefore#Circles A and B do not intersect at all.