Consider the curves, $x^2+y^2=1$ and $(x-1)^2+y^2=1.$ Points of intersection of two curves are :

$(0, ±1)$ $(0, ±\frac{\sqrt{3}}{2})$ $(\frac{1}{2}, ±\frac{\sqrt{3}}{2})$ $( ±1, 0)$

$(\frac{1}{2}, ±\frac{\sqrt{3}}{2})$