# Circle A has a center at (5 ,12 ) and an area of 81 pi. Circle B has a center at (1 ,2 ) and an area of 16 pi. Do the circles overlap? If not, what is the shortest distance between them?

Dec 19, 2017

Both the circles overlap as sum of the radii is greater than the difference between the centers

#### Explanation:

Radius of circle A ${r}_{1} = \sqrt{\frac{81 \pi}{\pi}} = 9$

Radius of circle B ${r}_{2} = \sqrt{\frac{16 \pi}{\pi}} = 4$

Distance between the centers of the two circles $d = \sqrt{{\left(5 - 1\right)}^{2} + {\left(12 - 2\right)}^{2}} = \sqrt{116} = 10.7703$

${r}_{1} + {r}_{2} = 9 + 4 = 13 i s > 10.7703 \left(d\right)$

Both the circles overlap as ${r}_{1} + {r}_{2} > d$