Question

which of the lines or segments below is a chord of circle o? answer attempt 1 out of 2
$overleftrightarrow{us}$
$overline{tu}$
$overline{ko}$
$overleftrightarrow{tr}$

Explanation:

Step1: Recall the definition of a chord

A chord of a circle is a line segment with both endpoints on the circle.

Step2: Analyze each option

• $\overleftrightarrow{US}$: This is a tangent line (touches the circle at one point \( U \) and \( S \) is on the other circle), so not a chord of circle \( O \).
• $\overline{TU}$: Both \( T \) and \( U \) are on circle \( O \), so this is a line segment with endpoints on circle \( O \), so it is a chord.
• $\overline{KO}$: \( O \) is the center of circle \( O \), \( K \) is on the circle, but \( O \) is the center (not on the circumference in the way a chord requires? Wait, no, the center is inside the circle. Wait, a chord must have both endpoints on the circle. \( O \) is the center, so \( \overline{KO} \) has one endpoint \( K \) on the circle and \( O \) inside, so not a chord.
• $\overleftrightarrow{TR}$: This is a line passing through \( T \) (on circle \( O \)) and \( R \) (on the other circle), but it's a line, not a segment with both endpoints on circle \( O \). Also, it's a line, not a segment. And \( R \) is not on circle \( O \).

Answer:

$\overline{TU}$