*The surfaces $\displaystyle z=\sqrt{x^2+y^2}$ and $\displaystyle x^2+y^2+z^2=1, z\geq$ intersect along a horizontal circle. Find an equation describing this circle. The angle between their normals at the intersection points never changes. What is this angle?*
And the hint is an intersection line of two surfaces, $\displaystyle f(x,y,z)=0$ and $\displaystyle g(x,y,z)=0$, is obtained as a solution of two simultaneous equations $\displaystyle f(x,y,z)=0$, $\displaystyle g(x,y,z)=0$, but I have no idea how to solve that