Two tangents each intersect a circle at opposite endpoints of the same diameter. Is it possible for the two tangents to intersect each other outside the circle? Explain why or why not, using the information you learned in this lesson.

Answer:

No, it is not possible for the two tangents to intersect. By definition, a tangent is perpendicular to the radius at the point of tangency. Since the tangents are at opposite endpoints of the same diameter, they are both perpendicular to the same line (the diameter). Therefore, the two tangent lines are parallel and will never intersect. Alternatively, the measure of the angle formed by two tangents is half the difference of the intercepted arcs. If the endpoints are a diameter, both arcs are 180 degrees, and half of (180 180) is 0, meaning no angle or intersection is formed.