Circle A has a center at $(5 ,3 )$ and an area of $54 pi$ . Circle B has a center at $(7 ,8 )$ and an area of $15 pi$ . Do the circles overlap?

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Answer 1 · 2016-04-16T03:09:20

**Let Radius of 1st circle be $r_1$ and 2nd circle be $r_2**$

$pixxr_1^2=54pi =>r_1=sqrt54=3sqrt6~~7.35$
$pixxr_2^2=15pi =>r_2=sqrt15=3.87$

The distance between the centers of the circles
$d=sqrt((5-7)^2+(3-8)^2)=sqrt29=5.39$

Here it is found $d cancel(>=)r_1+r_2$ So there will be overlap

Circle A has a center at (5 ,3 )(5 ,3 ) and an area of 54 pi54 pi. Circle B has a center at (7 ,8 )(7 ,8 ) and an area of 15 pi15 pi. Do the circles overlap?