Geometry worksheet illustrating the parts of a circle with diagrams and exercises for identifying terms like center, radius, diameter, chord, tangent, and secant.

Problem Analysis:

The worksheet focuses on identifying and understanding the different parts of a circle. We will solve each section step by step, using the provided diagrams and definitions.

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Section 1: Give an example of each circle part using the diagram below

#### Diagram:
The first diagram shows a circle with various labeled points and lines. We need to identify the following parts of the circle:

1. Center: The point at the center of the circle.
2. Radius: A line segment from the center to any point on the circle.
3. Chord: A line segment connecting two points on the circle.
4. Diameter: A chord that passes through the center of the circle.
5. Secant: A line that intersects the circle at two points.
6. Tangent: A line that touches the circle at exactly one point.
7. Point of Tangency: The point where the tangent touches the circle.
8. Minor Arc: An arc that is less than a semicircle.
9. Major Arc: An arc that is greater than a semicircle.
10. Semicircle: An arc that is exactly half of the circle.
11. Central Angle: An angle whose vertex is at the center of the circle.
12. Inscribed Angle: An angle whose vertex is on the circle and whose sides are chords of the circle.

#### Solution:
Using the first diagram:
- a) Center: \( K \)
- b) Radius: \( KG \), \( KH \), \( KI \), \( KJ \), or \( KL \)
- c) Chord: \( GH \), \( JL \), etc.
- d) Diameter: \( GL \) (since it passes through the center \( K \))
- e) Secant: Any line that intersects the circle at two points (e.g., the extension of \( GH \))
- f) Tangent: A line touching the circle at exactly one point (not explicitly shown in this diagram)
- g) Point of Tangency: The point where the tangent touches the circle (not explicitly shown in this diagram)
- h) Minor Arc: \( \overset{\frown}{GH} \) (less than a semicircle)
- i) Major Arc: \( \overset{\frown}{GHL} \) (greater than a semicircle)
- j) Semicircle: \( \overset{\frown}{GL} \) (exactly half of the circle)
- k) Central Angle: \( \angle GKH \) (vertex at the center \( K \))
- l) Inscribed Angle: \( \angle GJL \) (vertex on the circle)

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Section 2: Match the part of the circle with the term that best describes it

#### Diagram:
The second diagram shows a circle with labeled points and lines. We need to match each labeled part with its corresponding term.

1. GH: This is a diameter because it passes through the center \( M \).
2. M: This is the center of the circle.
3. MJ: This is a radius because it connects the center \( M \) to a point on the circle.
4. J: This is a point on the circle.
5. MH: This is a radius because it connects the center \( M \) to a point on the circle.
6. GH: This is a diameter because it passes through the center \( M \).
7. GH: This is a diameter because it passes through the center \( M \).

#### Solution:
- 2. GH: C. Diameter
- 3. M: A. Center
- 4. MJ: D. Radius
- 5. J: B. Chord (Note: \( J \) is a point, but it can be part of a chord)
- 6. MH: D. Radius
- 7. GH: C. Diameter

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Section 3: Identifying Terms

#### Diagram:
The third diagram shows a circle with labeled points and lines. We need to identify the term that best describes each given line, segment, or point.

1. CD: This is a chord because it connects two points on the circle.
2. FG: This is a tangent because it touches the circle at exactly one point.
3. EC: This is a secant because it intersects the circle at two points.
4. AB: This is a diameter because it passes through the center of the circle.
5. H: This is a point on the circle.
6. A: This is the center of the circle.

#### Solution:
- 21. CD: B. Chord
- 22. FG: F. Tangent
- 23. EC: E. Secant
- 24. AB: C. Diameter
- 25. H: B. Chord (Note: \( H \) is a point, but it can be part of a chord)
- 26. A: A. Center

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Final Answer:

\[
\boxed{
\begin{array}{ll}
\text{1.} & \text{a) Center: } K, \text{ b) Radius: } KG, \text{ c) Chord: } GH, \text{ d) Diameter: } GL, \text{ e) Secant: } \text{(any line intersecting at two points)}, \\
& \text{f) Tangent: } \text{(not shown)}, \text{ g) Point of Tangency: } \text{(not shown)}, \text{ h) Minor Arc: } \overset{\frown}{GH}, \text{ i) Major Arc: } \overset{\frown}{GHL}, \\
& \text{j) Semicircle: } \overset{\frown}{GL}, \text{ k) Central Angle: } \angle GKH, \text{ l) Inscribed Angle: } \angle GJL. \\
\text{2.} & \text{2) GH: C, 3) M: A, 4) MJ: D, 5) J: B, 6) MH: D, 7) GH: C.} \\
\text{3.} & \text{21) CD: B, 22) FG: F, 23) EC: E, 24) AB: C, 25) H: B, 26) A: A.}
\end{array}
}
\]