Question

which of the lines or segments below is secant to circle o?
answer attempt 1 out of 2
\\( \overline { z o } \\)
\\( \overleftrightarrow { z y } \\)
\\( \overleftrightarrow { d a } \\)
\\( \overline { l r } \\)

Explanation:

Step1: Recall the definition of a secant

A secant is a line that intersects a circle at two points.

Step2: Analyze each option

• $\overline{ZO}$: This is a radius (a line segment from the center of the circle to a point on the circle), it intersects the circle at only one point ($Z$).
• $\overleftrightarrow{DA}$: This line intersects circle $O$ at only one point ($D$) (it is a tangent to circle $O$ as it touches the circle at exactly one point).
• $\overleftrightarrow{ZY}$: This line intersects circle $O$ at two points ($Z$ and $L$), so it is a secant.
• $\overline{LR}$: This is a line segment, not a line that extends infinitely. A secant is a line (not just a segment), and $\overline{LR}$ does not intersect the circle at two points in the context of the definition of a secant (a secant is a line, and the segment $\overline{LR}$ is part of a line, but by itself, if we consider the geometric definition of a secant as an infinite - line intersecting a circle at two points, $\overline{LR}$ does not meet the criteria).

Answer:

$\overleftrightarrow{ZY}$