Circle A has a radius of 2 and a center at (5 ,6 ). Circle B has a radius of 5 and a center at (3 ,4 ). If circle B is translated by <-2 ,1 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?

1 Answer
Sep 28, 2016

The circles overlap.

Explanation:

If circle B with center (3,4) is translated by <-2,1> its new center will be at (3-2,4+1)=(1,5)
The distance between the center of A at (5,6) and the new center of B is given by the Pythagorean Theorem as:
color(white)("XXX")d=sqrt((5-1)^2+(6-5)^2)=sqrt(17)~~4.123

We are told that circle A has a radius of 2 and circle B has a radius of 2 and circle B has a radius of 5.

Considering the line segment joining the centers of the two circles,
we can see that A covers 2 units of that line segment and B covers 5 units (actually more than the length of the line segment.

Since there is only 4.123 units between the two centers, the circles must overlap.
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