Circle A has a center at #(3 ,4 )# and an area of #64 pi#. Circle B has a center at #(1 ,12 )# and an area of #54 pi#. Do the circles overlap?

1 Answer
May 7, 2018

The circles will intersect at two points.

Explanation:

Area of circle #A# is #A_A=pi *r_A^2= 64 pi :. r_A=8#

Area of circle #B# is #A_B=pi *r_B^2= 54 pi #

# :. r_B=sqrt 54~~7.35 (2dp) :. r_A+r_B= 15.35 #

and # |r_A-r_B| = 0.65#

Center of first circle #A# is at #(3,4)# and radius is #8# unit .

Center of second circle #B# is at #(1,12)# and radius is

#sqrt 54# unit . Distance between their centres is

#d=sqrt((x_1-x_2)^2+(y_1-y_2)^2)=sqrt((3-1)^2+(4-12)^2) # or

#d=sqrt(4+64)=sqrt 68 ~~ 8.25# unit.

Two circles intersect if, and only if, the distance between their

centers is between the sum and the difference of their radii.

Here #0.65 < 8.25 <15.35#, so they intersect at two points. [Ans]