Can the construction of a tangent line through a point be done with A inside circle C?

No, a tangent line cannot be constructed through a point A that lies inside circle C. A tangent line to a circle must touch the circle at exactly one point, and if point A is inside the circle, it cannot be tangent to any point on the circle. Instead, a line can be drawn from point A to the circle, but it will intersect the circle at two points rather than being tangent.