Circle A has a center at #(2 ,3 )# and an area of #72 pi#. Circle B has a center at #(14 ,5 )# and an area of #48 pi#. Do the circles overlap?

1 Answer
Nov 22, 2016

Answer:

Yes

Explanation:

The area of the first circle is#pi r^2=72pi#
#r=sqrt72#
#r=6sqrt2# =8.48 (2dp)
The area of the second circle is #pir^2= 48pi#
#r=sqrt48#
#r=4sqrt3#=6.93 (2dp)

The distance between the centres of the circles is found using Pythagoras.
The distance between the x coordinates is 12.
The distance between the y coordinates is 2
Draw the triangle . The length of the hypotenuse is #sqrt(12^2+2^2)#

=#sqrt148# =12.17(2dp)

If the circles did not overlap the the distance between their centres would have to be greater than the sum of the radii.
It is less so the circles overlap.