Circle A has a center at (2 ,2 ) and an area of 18 pi. Circle B has a center at (13 ,6 ) and an area of 27 pi. Do the circles overlap?

1 Answer
Oct 27, 2016

There is no Overlap

Explanation:

so we have two circles,

A, with centre (2,2) and Area 18pi
B, with centre (13,6) and Area 27pi

We will work with A first

A=pir^2

18pi=pir^2

r=sqrt(18) = 3*sqrt(2)

Now B,

27pi=pir^2

r=sqrt(27) = 3*sqrt(3)

so if they overlap the distance between the centres of the circles will be less than the two radii.

Distance between the two circles,

vec(AB)=B-A

=(13,6)-(2,2)

=(11,4)

Using Pythagoras theorem,

Distance = sqrt(a^2+b^2)

=sqrt(11^2+4^2)

=sqrt(137)

Now to find out,
To overlap this must be true,

sqrt(137) < r_"A"+r_"B"

sqrt(137) < 3*sqrt(2)+3*sqrt(3)

11.7047<4.2426+5.1962

11.7047<9.4388

This is not true so there is no Overlap.

Visually,

GeogebraGeogebra

The line f is longer than the two radii combined.