Tangency
= Tangency
Two smooth <curves> have <tangency> at a shared point when their <tangent lines> agree. A tangent to a <circle> is perpendicular to its radius at the contact point: at $(r,0)$ on $x^2+y^2=r^2$ the tangent is $x=r$. For smooth <surfaces> the analogous condition uses <tangent planes>. Tangency is local and does not preclude crossing: $y=0$ and $y=x^3$ have the same <tangent line> at zero but pass through one another there.