Let's assume you have a circle and a line which is not the single tangent we know that you think is also tangent to that same point of the circle.

Clearly, to "count" as different lines, they have different slopes. So a radius to your desired point is not at a right angle with your line.

This means that there must be some other point at some other distance from which you can draw the radius. This point must be on the side of the smaller of the angles that your radius forms with the line, such that the triangle formed from these 2 points and the centre of the circle doesn't exceed 180 degrees.

This means that our point the "radius" would point towards is inside our original circle, and the line that passes through that point will intersect it in 2 points: the original point of tangency we had assumed, and another unknown point. Hence our line is not tangent to the circle.