A tangent to a circle is defined as a line that intersects the circle at one and only one point. Such a line cannot be drawn through a circle as a circle is a closed geometric figure. If a line is drawn within a circle it has to touch the circle at two points, one point it enters the circle from and the other from which it emerges. The line is therefore not a tangent.
There are no lines that can be drawn through a circle and which are tangential to it.
Exactly 0 tangents can be drawn through a circle. A tangent intersects a circle in only one point so it does not actually enter the area of the circle. An infinite number of tangents to a given circle can be drawn since their is no limit to the points a tangent could intersect.
If an elipse were drawn inside a circle, then tangents to the elipse could be drawn through the circle.
With that in mind, a very large number of elispi (elipses? elipsefem?) could be drawn through the circle.
If a tetrahedron were drawn so that three of its edges intesected the circle, would they be tangent to the circle?