# Circle A has a center at (3 ,4 ) and an area of 18 pi. Circle B has a center at (8 ,1 ) and an area of 40 pi. Do the circles overlap?

Feb 10, 2018

Circles Overlap

#### Explanation:

Distance between the centers of the circles using distance formula

$\vec{{O}_{A} {O}_{B}} = \sqrt{{\left(8 - 3\right)}^{2} + {\left(1 - 4\right)}^{2}} \approx 5.83$

${A}_{A} = \pi {\left({R}_{A}\right)}^{2}$

${R}_{A} = \sqrt{\frac{18 \pi}{\pi}} \approx 4.24$

Similarly ${R}_{B} = \sqrt{\frac{40 \pi}{\pi}} \approx 6.32$

Sum of the radii ${R}_{A} + {R}_{B} = 4.24 + 6.32 = 10.56$

Since ${R}_{A} + {R}_{B} > \vec{{O}_{A} {O}_{B}}$, two circles overlap.