jmc

Question

You have two circles, one with radius r and the other with radius R. You wish for the difference in the areas of these two circles to be less than or equal to 5. If r+R=10, what is the maximum difference in the lengths of the radii?

Accepted Answer

We want R^2- r^2 5. Dividing by , we have R^2-r^2 5. Factor the left-hand side to get (R+r)(R-r) 5. Substituting 10 for R+r gives 10(R-r) 5 R-r 1/2. So the maximum difference in the lengths of the radii is 12.