Circle A has a center at #(1 ,5 )# and a radius of #3 #. Circle B has a center at #(2 ,-3 )# and a radius of #5 #. Do the circles overlap? If not, what is the smallest distance between them?

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Answer 1 · 2016-02-23T17:18:23

They do not overlap.

To overlap the distance between centres has to be less than the sum of their radii.

Let the sum of radii be #r#
Let the distance between radii be #d#

#"Centre"_"A" -> (x_1,y_1)->(1,5)#
#"Centre"_"B"->(x_2,y_2)->(2,-3)#

Sum of radii #-> 3+5=8 =r#

#color(blue)("Distance between centres")#

Using Pythagoras

#d^2 = (x_2-x_1)^2+(y_2-y_1)^2#

#d=+-sqrt((2-1)^2+(-3-5)^2)#

#d=+-sqrt(1^2+(-8)^2)" "=" "+-8.062# to 3 decimal places

As we are comparing sizes the #+-# does not have any significance.

As #d>s# the do not overlap