# 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?

Nov 22, 2016

Yes

#### Explanation:

The area of the first circle is$\pi {r}^{2} = 72 \pi$
$r = \sqrt{72}$
$r = 6 \sqrt{2}$ =8.48 (2dp)
The area of the second circle is $\pi {r}^{2} = 48 \pi$
$r = \sqrt{48}$
$r = 4 \sqrt{3}$=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 $\sqrt{{12}^{2} + {2}^{2}}$

=$\sqrt{148}$ =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.