Tangency is first-order contact between geometric objects at a common point. Two differentiable plane curves are tangent at a common point if their tangent lines there coincide. Two regular surfaces are tangent if their tangent planes coincide at the common point.
For a circle, a line is tangent when it is perpendicular to the radius at their common
point. Merely having a single common point
is not sufficient for tangency in general. For example, the lines 
and 
intersect only at the origin but are not tangent. Conversely,
tangency need not prevent crossing: the curves 
and 
cross at the origin even though they have the same tangent
line there.
