Question

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 1

No. Let O be the center and A, B the endpoints of the diameter. The radius OA is perpendicular to the tangent at A, and OB is perpendicular to the tangent at B. But OA and OB lie on the same line (they form the diameter), so both tangents are perpendicular to the same line and therefore are parallel. Parallel lines do not meet, so the two tangents cannot intersect anywhere outside the circle.