Circle A has a radius of #5 # and a center of #(5 ,2 )#. Circle B has a radius of #2 # and a center of #(4 ,5 )#. If circle B is translated by #<-3 ,4 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
They do not overlap, minimum distance is
First let's move the center of circle B.
Translation simply moves the circle's center, so we can just add the translation amount to the x and y values of the center.
So now we just need to figure out if A and B overlap.
B has a radius of 2, and A has a radius 5.
So, they will overlap if A's center and B's center are less than 7 away.
Distance from A's center to B's center can be calculated using distance formula.
The distance is greater than
If you do not have a calculator to calculate the square root, we know that
The minimum distance between the circles can be calculated by taking the difference of the distance and 7.
This is because a line drawn from one center to the other will be the length of both radii plus the minimum distance between the circles.