A tangent line touches a circle at how many points?

A tangent line touches a circle at how many points?

• A. Two points
• B. Zero points
• C. Infinitely many points
• D. One point

Answer: (D)

A tangent line to a circle touches it at exactly one point. That single point is the contact point, where the line just grazes the circle and does not pass through its interior. At the point of tangency, the radius drawn to that point is perpendicular to the tangent line, which helps explain why the line doesn’t cross the circle. If a line cuts through the circle, it would meet it in two points (a secant). If it doesn’t meet at all, there are zero intersections. An actual overlap of a line with the entire circle isn’t possible, since a circle is curved and a straight line cannot coincide with it, so you can’t have infinitely many shared points. Therefore the tangent line meets the circle at exactly one point.

A tangent line to a circle touches it at exactly one point. That single point is the contact point, where the line just grazes the circle and does not pass through its interior. At the point of tangency, the radius drawn to that point is perpendicular to the tangent line, which helps explain why the line doesn’t cross the circle. If a line cuts through the circle, it would meet it in two points (a secant). If it doesn’t meet at all, there are zero intersections. An actual overlap of a line with the entire circle isn’t possible, since a circle is curved and a straight line cannot coincide with it, so you can’t have infinitely many shared points. Therefore the tangent line meets the circle at exactly one point.