Circle A has a center at #(8 ,4 )# and a radius of #3 #. Circle B has a center at #(-1 ,-2 )# and a radius of #4 #. Do the circles overlap? If not, what is the smallest distance between them?
1 Answer
The circles are separate and there is a minimum distance between them of 3.82
Explanation:
The distance between the two centres can be calculated using this
formula which is derived from Pythagoras's theorem
substituting in the values from the question
Simplifying
subtracting the radii of the two circles from the distance between the two centres indicates whether they over lap, touch or are separate.
distance - radius A - radius B < 0 : the circles overlap
distance - radius A - radius B = 0 : the circles touch
distance - radius A - radius B > 0 : the circles are separate
In this case
The circles are separate and there is a minimum distance between them of 3.82