# Circle A has a center at (5 ,9 ) and an area of 65 pi. Circle B has a center at (7 ,2 ) and an area of 43 pi. Do the circles overlap?

Sep 22, 2017

The circles overlap

#### Explanation:

Let radius of circle A as R1 and that of circle B as R2.
Area of circle A is $\pi R {1}^{2} = 65 \pi$
$\therefore R {1}^{2} = 65$
$R 1 = \sqrt{65}$
Area of circle B is $\pi R {2}^{2} = 43 \pi$
$\therefore R {2}^{2} = 43$
$R 2 = \sqrt{43}$
Let us find the Distance between the circle centres (5,9) and (7,2)
Distance D = $\sqrt{{\left(5 - 7\right)}^{2} + {\left(9 - 2\right)}^{2}}$
$= \sqrt{- {2}^{2} + {7}^{2}}$
$= \sqrt{53}$
$R 1 + R 2 = \sqrt{65} + \sqrt{43} > D = \sqrt{53}$
Hence the circles overlap.