Question

in circle d, which is a secant? \\(\overline{dc}\\) \\(\overrightarrow{ab}\\) \\(\overline{ef}\\) \\(\overleftrightarrow{gh}\\)

Explanation:

Step1: Recall secant definition

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

Step2: Analyze each option

• $\overline{DC}$: A radius (connects center to circle), intersects at 1 point (C) and center D, not a secant.
• $\overrightarrow{AB}$: A tangent (intersects at 1 point B), not a secant.
• $\overline{EF}$: A chord (segment with both endpoints on circle), not a line (secant is a line, chord is segment), so not a secant.
• $\overleftrightarrow{GH}$: A line intersecting circle at G and H (two points), so it's a secant. Wait, wait, the last option is $\overleftrightarrow{GH}$? Wait the options: let's recheck. Wait the options are $\overline{DC}$, $\overrightarrow{AB}$, $\overline{EF}$, $\overleftrightarrow{GH}$? Wait the user's options: the last one is $\overleftrightarrow{GH}$? Wait in the image, the last option is $\overleftrightarrow{GH}$? Wait the user's text: the last option is $\overleftrightarrow{GH}$? Wait the original problem's options:

Wait the options given:

1. $\overline{DC}$: segment from D (center) to C (on circle) – radius, intersects at 1 point (C) and D (inside), not two on circle.

1. $\overrightarrow{AB}$: ray starting at A, touching B (tangent, 1 point).

1. $\overline{EF}$: segment with E and F on circle – chord (segment), not a line (secant is a line, chord is segment).

1. $\overleftrightarrow{GH}$: line passing through G and H (both on circle) – intersects at two points, so secant.

Wait but maybe I misread. Wait the user's options: the last one is $\overleftrightarrow{GH}$? Wait the user's text: the last option is $\overleftrightarrow{GH}$? Let's check again.

Wait the user's problem:

Options:

• $\overline{DC}$

• $\overrightarrow{AB}$

• $\overline{EF}$

• $\overleftrightarrow{GH}$

So:

• $\overline{DC}$: radius (segment, 1 point on circle, 1 at center) – not secant.

• $\overrightarrow{AB}$: tangent (ray, 1 point) – not secant.

• $\overline{EF}$: chord (segment, 2 points on circle) – but secant is a line, chord is segment. So secant is a line, chord is segment. So $\overleftrightarrow{GH}$ is a line (since it's a line with arrows, $\overleftrightarrow{GH}$) intersecting at G and H – two points. So that's the secant.

Wait but maybe the last option is $\overleftrightarrow{GH}$? So the correct answer is $\overleftrightarrow{GH}$, which is the last option.

Wait the user's options: the last one is $\overleftrightarrow{GH}$? Let's confirm the definitions:

• Secant: A line that intersects a circle at two points.

• Tangent: A line that intersects a circle at exactly one point.

• Chord: A segment with both endpoints on the circle.

• Radius: A segment from center to circle.

So:

• $\overline{DC}$: radius (segment, 1 point on circle, 1 at center) – not secant.

• $\overrightarrow{AB}$: tangent (ray, 1 point) – not secant.

• $\overline{EF}$: chord (segment, 2 points on circle) – but it's a segment, not a line. Secant is a line, so chord is a segment, secant is a line containing a chord.

• $\overleftrightarrow{GH}$: line (since it's a line with arrows) intersecting circle at G and H – two points, so secant.

Thus, the correct option is the last one, $\overleftrightarrow{GH}$.

Answer:

$\overleftrightarrow{GH}$ (the last option, labeled as $\overleftrightarrow{GH}$)