# Circle A has a center at (1 ,4 ) and an area of 28 pi. Circle B has a center at (7 ,9 ) and an area of 8 pi. Do the circles overlap? If not, what is the shortest distance between them?

Feb 10, 2018

Since sum of radii greater than the distance between the centers, Circles Overlap

#### Explanation:

Given : Circle A - O_A 91,4), A_A = 28pi, Radius ${R}_{A}$

Circle B - ${O}_{B} \left(1 , 4\right) , {A}_{B} = 28 \pi$, Radius ${R}_{B}$

${R}_{A} = \sqrt{{A}_{A} / \pi} = \sqrt{\frac{28 \pi}{\pi}} \approx 5.29$

${R}_{B} = \sqrt{{A}_{B} / \pi} = \sqrt{\frac{8 \pi}{\pi}} \approx 2.83$

Sum of Radii R_A + R_B = 5.29 + 2.83 = color(red)(8.12

Using distance formula,

vec(O_AO_B) = sqrt((7-1)^2 + (9-4)^2) ~~ color(red)(7.81

Since sum of radii greater than the distance between the centers, Circles Overlap