# Circle A has a center at (7 ,5 ) and an area of 92 pi. Circle B has a center at (9 ,2 ) and an area of 14 pi. Do the circles overlap?

Mar 11, 2016

They will overlap,practically smaller one will be inside larger

#### Explanation:

Given
Area of 1st circle $= 92 \pi = \pi {r}_{1}^{2}$ , where ${r}_{1}$=radius of 1st circle
Hence ${r}_{1} = \sqrt{92}$
Again Area of 2nd circle $= 14 \pi = \pi {r}_{2}^{2}$ , where ${r}_{2}$=radius of 2nd circle
Hence ${r}_{1} = \sqrt{14}$
Sum of their radii $S = {r}_{1} + {r}_{2} = \sqrt{92} + \sqrt{14}$

Now the distance between their centers
$d = \sqrt{{\left(7 - 9\right)}^{2} + {\left(5 - 2\right)}^{2}} = \sqrt{13} =$
S>d => They will overlap,practically smaller one will be inside larger one because ${r}_{2} - {r}_{1} > d$