# Circle A has a center at (3 ,7 ) and an area of 56 pi. Circle B has a center at (9 ,6 ) and an area of 28 pi. Do the circles overlap?

Mar 15, 2016

the circles will overlap.

#### Explanation:

the circles will overlap if the distance between the centers is smaller than the sum of the radius.

the distance between the radius is,

$d = \sqrt{{\left(9 - 3\right)}^{2} + {\left(7 - 6\right)}^{2}}$

$= \sqrt{{6}^{2} + {1}^{2}}$

$= \sqrt{36 + 1}$

$= 6.08$

here,

$\pi {r}_{1}^{2} = 56 \pi$

$\mathmr{and} , {r}_{1}^{2} = 56$

$\mathmr{and} , {r}_{1} = 7.48$

again,

$\pi {r}_{2}^{2} = 28 \pi$

$\mathmr{and} , {r}_{2}^{2} = 28$

$\mathmr{and} , {r}_{2} = 5.29$

so,
${r}_{1} + {r}_{2} = 7.48 + 5.29$

$= 12.77$

so, the circles will overlap.