problem 1059
On a paper, draw a circle and a secant PQ of the circle. Draw various lines parallel to the secant on both sides of it. You will find that after some steps, the length of the chord cut by the lines will gradually decrease, i.e., the two points of intersection of the line and the circle are coming closer and closer. In one case, it becomes zero on one side of the secant and in another case, it becomes zero on the other side of the secant. See the positions P'Q' and P''Q'' of the secant. These are the tangents to the circle parallel to the given secant PQ. This also helps you to see that there cannot be more than two tangents parallel to a given secant.