There cannot be more than two tangents to a circle parallel to a given secant.
Maximum number of tangents to a circle which are parallel to a secant can be two.
At most two tangents can be drawn parallel to a given secant because there are only two points on a circle through which the lines parallel to the secant are tangents to the circle.
If a secant is drawn to a circle, then under any circumstance, tangents cannot be drawn parallel to the secant.