Circle A has a center at (5 ,-4 ) and a radius of 7 . Circle B has a center at (-6 ,-8 ) and a radius of 5 . Do the circles overlap? If not, what is the smallest distance between them?

Apr 1, 2016

overlap

Explanation:

First step is to calculate the distance between the centres using the $\textcolor{b l u e}{\text{ distance formula }}$

 d = sqrt((x_2 - x_!)^2 + (y_2 - y_1)^2)

where $\left({x}_{1} , {y}_{1}\right) \text{ and " (x_2,y_2)" are 2 coordinate points }$

let $\left({x}_{1} , {y}_{1}\right) = \left(5 , - 4\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(- 6 , - 8\right)$

$d = \sqrt{{\left(- 6 - 5\right)}^{2} + {\left(- 8 - \left(- 4\right)\right)}^{2}} = \sqrt{{\left(- 11\right)}^{2} + {\left(- 4\right)}^{2}}$

= sqrt(121 + 16) = sqrt137 ≈ 11.7

now, radius of A + radius of B = 7 + 5 = 12

Since , sum of radii > distance between centres , circles
overlap.