# 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 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.