How many points does a secant intersect a circle?

A secant line intersects a circle at exactly two distinct points. By definition, a secant is a line that passes through the interior of a circle, connecting two points on the circle itself. When such a line is drawn, it will cut through the circle, entering at one point and exiting at another, thereby creating two points of intersection.

This characteristic is fundamental in geometry and differentiates secants from other types of lines. For example, a tangent line, which touches the circle at exactly one point, behaves differently from a secant, reinforcing the unique nature of secant lines.

The other options do not correctly describe the behavior of secants with respect to circles. One point indicates a tangent, three points would imply some form of higher intersection not possible with standard secants, and infinitely many points would suggest a line that entirely lies on the circumference, which is not a secant. Thus, the correct understanding of how a secant interacts with a circle allows us to confidently assert that it intersects at two points.