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?
The area of the first circle is
The area of the second circle is
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
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.