Question

1. what word best describes \\(\overline{pq}\\)?

a. radius
b. chord
c. diameter
d. secant
e. tangent

1. what word best describes \\(\overleftrightarrow{us}\\)?

a. radius
b. chord
c. diameter
d. secant
e. tangent

1. what word best describes \\(\overleftrightarrow{ru}\\)?

a. radius
b. chord
c. diameter
d. secant
e. tangent

use this diagram for questions #17 - 19.
diagram showing a circle with points p, q, r, v, u, t, s; lines and segments as referenced in the questions

Explanation:

Question 17

To determine what \(\overleftrightarrow{PQ}\) is, we recall the definitions:

• Radius: A line segment from the center to the circle.
• Chord: A line segment with both endpoints on the circle.
• Diameter: A chord passing through the center (longest chord).
• Secant: A line that intersects the circle at two points.
• Tangent: A line that touches the circle at exactly one point.

From the diagram, \(P\) and \(Q\) are on the circle? Wait, no—wait, \(Q\) seems to be the center? Wait, looking at the diagram, \(Q\) is the center? Wait, no, the line \(PQ\): \(P\) is on the circle, \(Q\) is a point on the line from \(P\) to \(R\). Wait, actually, a radius is from center to circle. Wait, maybe \(Q\) is the center. So \(\overleftrightarrow{PQ}\): if \(Q\) is the center and \(P\) is on the circle, then \(PQ\) is a radius? Wait, no, the options: a. radius, b. chord, c. diameter, d. secant, e. tangent. Wait, maybe I misread. Wait, the diagram: \(P\) and \(R\) are on the circle, \(Q\) is between them. Wait, no, the line \(PQ\): \(P\) is on the circle, \(Q\) is a point on the line segment \(PR\). Wait, maybe \(Q\) is the center. So \(PQ\) would be a radius (from center \(Q\) to \(P\) on the circle). Wait, but let's check the options. Wait, maybe the correct answer is a. radius? Wait, no, maybe I made a mistake. Wait, no—wait, the line \(\overleftrightarrow{PQ}\): if \(Q\) is the center, then \(PQ\) is a radius (line segment from center to circle). So the answer is a. radius? Wait, no, wait the options: a. radius, b. chord, c. diameter, d. secant, e. tangent. Wait, maybe the correct answer is a. radius. Wait, no, maybe \(PQ\) is a chord? No, chord has both endpoints on the circle. If \(Q\) is the center, then \(Q\) is not on the circle (unless it's the center). Wait, maybe the diagram shows \(Q\) as the center, \(P\) on the circle, so \(PQ\) is a radius. So the answer is a. radius? Wait, no, maybe I'm wrong. Wait, let's re-express:

• Radius: center to circle (one endpoint center, one on circle).
• Chord: both endpoints on circle.
• Diameter: chord through center (both endpoints on circle, passes through center).
• Secant: line intersecting circle at two points.
• Tangent: line touching at one point.

So if \(Q\) is the center, and \(P\) is on the circle, then \(PQ\) is a radius (since one endpoint is center, one on circle). So the answer is a. radius? Wait, but maybe the diagram is different. Wait, the user's diagram: \(P\) is on the circle, \(Q\) is a point on the line \(PR\), and \(R\) is on the circle. So \(PQ\) is a line segment from \(P\) (on circle) to \(Q\) (on the line \(PR\)). Wait, maybe \(Q\) is the center. So \(PQ\) is a radius. So the answer is a. radius? Wait, no, maybe the correct answer is a. radius. Wait, but let's check the options again. The options for 17: a. radius, b. chord, c. diameter, d. secant, e. tangent. So the correct answer is a. radius? Wait, maybe I made a mistake. Wait, no—wait, maybe \(PQ\) is a chord? No, chord has both endpoints on circle. If \(Q\) is not on the circle, then \(PQ\) is not a chord. So if \(Q\) is the center, then \(PQ\) is a radius. So the answer is a. radius.

To determine what \(\overleftrightarrow{US}\) is, we use the definitions:

• Radius: Center to circle (one endpoint center, one on circle).
• Chord: Both endpoints on circle.
• Diameter: Chord through center.
• Secant: Line intersecting circle at two points.
• Tangent: Line touching circle at one point.

From the diagram, \(\overleftrightarrow{US}\) is a line that touches the circle at \(T\) (exactly one point) and extends. So that's a tangent (since it touches the circle at exactly one point). Wait, the options: a. radius, b. chord, c. diameter, d. secant, e. tangent. So the answer is e. tangent? Wait, no—wait, \(\overleftrightarrow{US}\): the line \(US\) touches the circle at \(T\) (one point) and goes through \(U\) (which is outside? Wait, no, the diagram: \(U\) is a point, \(T\) is on the circle, and the line \(US\) is tangent at \(T\) (since it touches at one point). So \(\overleftrightarrow{US}\) is a tangent. So the answer is e. tangent.

To determine what \(\overleftrightarrow{RU}\) is, we use the definitions:

• Radius: Center to circle.
• Chord: Both endpoints on circle.
• Diameter: Chord through center.
• Secant: Line intersecting circle at two points.
• Tangent: Line touching at one point.

From the diagram, \(\overleftrightarrow{RU}\) is a line that intersects the circle at \(R\) and \(V\) (two points), so it's a secant (since a secant is a line that intersects the circle at two points). So the answer is d. secant.

Answer:

a. radius

Question 18