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

Yes

Explanation:

The area of the first circle ispi 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.