Circle A has a radius of #3 # and a center of #(3 ,9 )#. Circle B has a radius of #2 # and a center of #(1 ,4 )#. If circle B is translated by #<3 ,-1 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
No overlap between Circle A and Circle B. Minimum distance = 1.083. See explanation and the diagram below.
Compare the distance (d) between the centres of the circles to the sum of the radii.
1) If the sum of the radii
2) If the sum of the radii
The first step here is to calculate the new centre of B under the traslation, which does not change the shape of the circle only its' position.
Under a translation
To calculate d, use the distance formula :
here the two points are
Sum of radii = radius of A + radius of B
Since sum of radius
Min.D minimum distance (the red line in the daigram) :