Question

1. for exercises a-e, refer to the circle at the right.

a. name the circle
b. name the radii of the circle.
c. name the chords of the circle.
d. name a diameter of the circle
e. name a radius not drawn as part of a diameter.

Explanation:

Step1: Recall Circle Naming Rule

A circle is named by its center. The center here is \( T \), so the circle is named Circle \( T \) (or \( \odot T \)).

Step2: Recall Radius Definition

A radius is a segment from the center to a point on the circle. Center \( T \), points on circle: \( L \), \( M \), \( I \), \( J \), \( K \)? Wait, looking at the diagram: center \( T \), points \( L \), \( M \), \( I \), \( J \), \( K \)? Wait, the diagram has \( T \) as center, with segments \( TL \), \( TM \), \( TI \), \( TJ \)? Wait, no, the diagram shows \( L \) and \( M \) on a diameter, \( I \) connected to \( T \), \( J \) and \( K \) with a chord. So radii are segments from \( T \) to circle: \( TL \), \( TM \), \( TI \), \( TJ \)? Wait, no, let's check again. The circle has center \( T \). So radii are \( TL \), \( TM \), \( TI \) (wait, \( TI \) is a radius, \( TL \) and \( TM \) form a diameter, \( TJ \)? Wait, maybe \( TJ \) is a radius? Wait, the diagram: \( T \) is center, \( L \) and \( M \) are on a line through \( T \) (diameter \( LM \)), \( I \) is on the circle with \( TI \) (radius), \( J \) and \( K \) with chord \( JK \). So radii: \( TL \), \( TM \), \( TI \), \( TJ \)? Wait, maybe \( TJ \) is a radius? Wait, no, let's do each part:

Part a: Name the circle

A circle is named by its center. The center is \( T \), so the circle is \( \odot T \) (Circle \( T \)).

Part b: Name the radii

Radius: segment from center (\( T \)) to circle. So \( TL \), \( TM \), \( TI \), \( TJ \)? Wait, no, looking at the diagram: \( L \) and \( M \) are on a diameter (so \( TL \) and \( TM \) are radii), \( I \) is connected to \( T \) (radius \( TI \)), \( J \) is on the circle, so \( TJ \) is a radius? Wait, maybe \( TJ \) is a radius. So radii: \( \overline{TL} \), \( \overline{TM} \), \( \overline{TI} \), \( \overline{TJ} \)? Wait, maybe \( TJ \) is a radius. Let's confirm: radius is center to circle, so any segment from \( T \) to a point on the circle. So \( TL \), \( TM \), \( TI \), \( TJ \) (if \( J \) is on the circle) or \( TK \)? Wait, the diagram has \( J \) and \( K \) with chord \( JK \), so \( J \) and \( K \) are on the circle. So radii: \( \overline{TL} \), \( \overline{TM} \), \( \overline{TI} \), \( \overline{TJ} \), \( \overline{TK} \)? Wait, maybe the diagram shows \( J \) and \( K \) with chord \( JK \), \( L \) and \( M \) with diameter \( LM \), \( I \) with radius \( TI \). So radii: \( \overline{TL} \), \( \overline{TM} \), \( \overline{TI} \), \( \overline{TJ} \) (if \( J \) is on circle) or \( \overline{TK} \). Wait, maybe the correct radii are \( \overline{TL} \), \( \overline{TM} \), \( \overline{TI} \), \( \overline{TJ} \)? Wait, no, let's check standard: radius is center to circumference. So center \( T \), points on circumference: \( L \), \( M \), \( I \), \( J \), \( K \). So radii: \( TL \), \( TM \), \( TI \), \( TJ \), \( TK \)? But maybe in the diagram, \( J \) and \( K \) are on the circle, \( L \), \( M \), \( I \) too. So radii: \( \overline{TL} \), \( \overline{TM} \), \( \overline{TI} \), \( \overline{TJ} \), \( \overline{TK} \)? Wait, maybe the diagram has \( T \) as center, with \( LM \) as diameter (so \( TL = TM \)), \( TI \) as radius, \( JK \) as chord, \( TJ \) as radius? Maybe I missee, but let's proceed.

Part c: Name the chords

A chord is a segment with both endpoints on the circle. So \( LM \) (diameter, hence chord), \( JK \), and any others? \( LM \), \( JK \), and maybe \( TI \)? No, \( TI \) has one endpoint at center (not a chord). So chords: \( LM \), \( JK \).

Part d: Name a diameter

A diameter is a chord passing through the center. \( LM \) passes through \( T \) (center), so \( LM \) (or \( \overline{LM} \)) is a diameter.

Part e: Name a radius not part of a diameter

Radii part of diameter: \( TL \), \( TM \) (since \( LM \) is diameter). So a radius not in a diameter: \( TI \) (or \( TJ \), \( TK \) if they exist). \( TI \) is a radius not part of \( LM \) (the diameter shown), so \( TI \).

Answer:

a. The circle is \( \boldsymbol{\odot T} \) (Circle \( T \)).
b. The radii are \( \boldsymbol{\overline{TL}} \), \( \boldsymbol{\overline{TM}} \), \( \boldsymbol{\overline{TI}} \), \( \boldsymbol{\overline{TJ}} \) (assuming \( J \) is on the circle; adjust based on diagram, but typically \( TL \), \( TM \), \( TI \), \( TJ \) or similar).
c. The chords are \( \boldsymbol{\overline{LM}} \) and \( \boldsymbol{\overline{JK}} \).
d. A diameter is \( \boldsymbol{\overline{LM}} \).
e. A radius not part of a diameter is \( \boldsymbol{\overline{TI}} \).