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Easy question about a system (or is it)


Question

Suppose we have the following system

x^2+y^2=r; x+y=r, such that the line crosses the circle at exactly two places. 

Obviously with two equations and three variables, we have a solution set of answers that can satisfy the given conditions.  What I want to know is of the given solutions that satisfies this problem, what is the smallest and largest values x can possibly be?

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I have a negative value for x as my min and a different x max

36 minutes ago, Nightfox__ said:

Max of x is 1/2+(1/√2) and min 0??

This is not the answer but as an example of this possibility:

image.png.d8df38712201e7e3883b7b0029c90d25.png

 

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1 hour ago, Nightfox__ said:

X comes around 1.207 at r = 1 + (1/ 2) . Are you saying a larger value of x is possible??

x.JPG

On the right track but see if you can find what x is approaching.

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