Question

question 23 of 25

which line segment is a chord of \\(\odot p\\) in the diagram below?

a. \\(\overline{rs}\\)

b. \\(\overline{qr}\\)

c. \\(\overline{pq}\\)

d. \\(\overline{st}\\)

Explanation:

Define a chord of a circle

A chord is a line segment whose endpoints both lie on the circle.

Analyze the given line segments

• \(\overline{RS}\): Point \(R\) lies on the circle, but point \(S\) lies outside the circle.
• \(\overline{QR}\): Both point \(Q\) and point \(R\) lie on the circle.
• \(\overline{PQ}\): Point \(P\) is the center of the circle, and point \(Q\) lies on the circle (this is a radius).
• \(\overline{ST}\): Point \(T\) lies on the circle, but point \(S\) lies outside the circle (this is a tangent segment).

Identify the correct option

Since both endpoints of \(\overline{QR}\) lie on circle \(P\), \(\overline{QR}\) is a chord.

Answer:

• A. \(\overline{RS}\)
• B. \(\overline{QR}\) (Correct answer)
• C. \(\overline{PQ}\)
• D. \(\overline{ST}\)