Circle A has a center at (5 ,4 ) and an area of 16 pi. Circle B has a center at (12 ,8 ) and an area of 25 pi. Do the circles overlap? If not, what is the shortest distance between them?

1 Answer
Oct 14, 2017

The given circles intersect

Explanation:

Since the area of a circle is pi*r^2

we get

16cancelpi=cancelpi*r^2 (circle A)

then r_A=4

and

25cancelpi=cancelpi*r^2 (circle B)

then

r_B=5

The distance between the centers is:

C_AC_B=sqrt((x_B-x_A)^2+(y_B-y_A)^2)

=sqrt((12-5)^2+(8-4)^2)=sqrt(49+16)=sqrt65

that's less than the sum of the radiuses

C_AC_B=sqrt65<4+5

We conclude that the circles intersect:

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