Distance Between 2 Circles w/ 1 Common Point: All Possible Values

[xstetsonx]

There are two circles in the plane, their radii are 2 and 5. It is known that they have EXACTLY ONE common point. List all possible values of the distance between their centers.

okay, i know if two circles touch by one point their center distance can be 7 but it says all possible valueS. I don't see any other solution for this question. Please help

 

[Mark44]

You are assuming that the circles are outside each other, and intersect at just one point. What if the smaller circle is inside the larger one?

 

[xstetsonx]

You are assuming that the circles are outside each other, and intersect at just one point. What if the smaller circle is inside the larger one?

but the question says the have only one common pt if the smaller circle is inside of the big one. don't they have more than one common point? Even if that is the case, it would be infinite right?

 

[Mark44]

The smaller (inside) circle would still intersect the larger one at only one point. Why do you think it (what is it?) is infinite?

 

[xstetsonx]

if so there are infinite answers to the distance between two circles' distance right?? could be from 7 to 0?

 

[Mark44]

I get only one value when one circle is inside the other.

 

[xstetsonx]

o i got it