Correct Response: B. For a second tangent line to be parallel to a first tangent line, it must be tangent to that circle at a point that is 180 degrees around the circle from the first tangent line. Any line that joins two points 180 degrees apart around a circle must be a diameter of that circle since it divides it perfectly in half. Therefore, choice B is correct. Choices A, C, and D all employ constructions that make use of the endpoints of the originally drawn tangent line. Since these endpoints are not defined in the problem, none of the resulting constructions are completely defined. Hence each construction could result in an infinite number of different drawings, most of which would not lead to the determination of the diameter of the circle.
