Circle A has a center at (1 ,8 ) and an area of 15 pi. Circle B has a center at (5 ,3 ) and an area of 24 pi. Do the circles overlap?

Oct 3, 2016

The distance between the centers is less than the sum of their radii, therefore, the circles overlap.

Explanation:

The area of a circle is A = pir². This allows us to observe that the radius of circle A is:

${r}_{a} = \sqrt{15}$

And the radius of circle B is:

${r}_{b} = \sqrt{24}$.

The distance, d, between the centers is:

d = sqrt((1 - 5)² + (8 - 3)²)

d = sqrt((-4)² + (5)²)

$d = \sqrt{16 + 25}$

$d = \sqrt{41}$

$d < \left({r}_{a} + {r}_{b}\right)$ by 2.369, therefore, the circles overlap