# Circle A has a center at (2 ,5 ) and a radius of 2 . Circle B has a center at (4 ,-1 ) and a radius of 6 . Do the circles overlap? If not, what is the smallest distance between them?

If you make a right angled triangle between the two centres, using the line that joins them as the hypotenuse. The height of the triangle is 6 and the base is 2. Using Pythagoras the hypotenuse would be $\sqrt{40}$ = approx 6.3 cm. If the distance between the centres is 6.3 and one radius is 6 and the other is 2 then they do overlap.