Question 268667
OUr two equations are
(i) {{{(x-1)^2 + y^2 = 1}}}
(ii) {{{x^2 + y^2 = r^2}}}
take (i) - (ii) to get
(iii) {{{(x-1)^2 - x^2 = 1 - r^2}}}
simplify to get
(iv) {{{-2x + 1 = 1 - r^2}}}
solving for x we get
(v) {{{r ^2/2}}}
now, we can find y as
(vi) y = {{{sqrt(r^2 - (r^4/4))}}}
or simplified to
(vii) y = {{{(r/2)*sqrt(1-r^2)}}}
Now, the y -intercept of C2 is (0,r).
---
Next we create an equation of a line passing through the y intercept of C2 and the crossing point of the two circles as
(viii) y = {{{((-2+2*sqrt(1-r^2))/r)X + r}}}  
We want the x intercept or the value of x when y = 0.
This is
(ix) x = {{{-r^2/(-2+2*sqrt(1-r^2))}}}
The limit of x as r -> 0, is 1
The root of the line tends to 1.