# Circle A has a center at (1 ,3 ) and an area of 45 pi. Circle B has a center at (2 ,7 ) and an area of 75 pi. Do the circles overlap?

Dec 19, 2017

Two circles overlap

#### Explanation:

Area of circle A = $\pi {r}_{1}^{2} = 45 \pi$

${r}_{1} = \sqrt{\frac{45 \pi}{\pi}} = \sqrt{45}$

Area of circle B = $\pi {r}_{2}^{2} = 75 \pi$

${r}_{2} = \sqrt{\frac{75 \pi}{\pi}} = \sqrt{75}$

Distance between the two centers $d = \sqrt{{\left(2 - 1\right)}^{2} + {\left(7 - 3\right)}^{2}} = \sqrt{17}$

Since the radii of the two circles are greater than the distance between the centers of the two circles, circles overlap.