Solve Nested Ball Problem: r_big-r_small ≤ d(x,y)

[robertdeniro]

Homework Statement

given a ball within another ball
show that the distances between their centers are less than the difference in their radii

Homework Equations

The Attempt at a Solution

let r_big and r_small represent the respective radii and let x and y represent the centers of the big and small balls

i got d(x,y)<=r_big+r_small by triangle inequality but i need r_big-r_small

 

[Dick]

Did you try and draw two circles in the plane where |x-y|>r_big-r_small and try to figure out why the smaller circle can't be contained in the larger circle? If you can explain that in words, then you are probably halfway there.

 

[robertdeniro]

nm i got it