Here is a Wikipedia article about tangent lines to circles. It states that
In Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior.
Does this definition also apply to lines that lie in different planes to that of the circle? I am not sure but I think that the definition of a tangent line to a circle is only applicable to lines that lie in the same plane as that of the circle as some properties of a tangent line tend to break down with a change in plane. For example if the centre and the point of contact of the tangent with the circle are joined, we get a line segment perpendicular to the tangent. This property is not always true if the plane is changed.
Now, my definition of a cone with a circular base uses the fact that tangent lines to a circle may be drawn from a point not lying in the circle's plane. According to it
A cone is a locus of all lines which intersect a circular base and a point not lying on it.
Can this be considered a definition of a cone?