Ohio Assessments for Educators (OAE) Mathematics Practice Exam

Which statement best defines a tangent line?

1. A line segment with endpoints inside the circle

2. A line that intersects the circle at two points

3. A line that passes through the center of the circle

4. A line that touches the circle at exactly one point

The correct answer is: A line that touches the circle at exactly one point

A tangent line is specifically defined as a line that touches a circle at exactly one point. This point of contact is referred to as the point of tangency. The key characteristic of a tangent line is that it does not cross into the circle; rather, it only meets the circle at that singular point. This distinct feature differentiates tangent lines from other types of lines in relation to circles. In contrast, a line segment with endpoints inside the circle depicts a line that is completely enclosed within the circle, which does not fit the definition of a tangent. A line that intersects the circle at two points would be classified as a secant line, not a tangent. Additionally, a line that passes through the center of the circle represents a diameter, which inherently intersects the circle at two points, thus also deviating from what constitutes a tangent line. Thus, defining a tangent line as one that interacts with the circle at just one point is accurate and captures its essence correctly.