Geometry worksheet focusing on identifying parts of a circle using diagrams and terminology.

Let's solve each part of this Geometry: Parts of a Circle Worksheet step by step, using the diagrams and definitions.

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

We are given a circle with points labeled:
- Points on the circle: G, H, I, J, L
- Center: K (since it's marked at the center)
- Lines: GH, HI, JL, etc.

#### a) Center:
The center is the point in the middle of the circle.
✔ Answer: K

#### b) Radius:
A radius is a segment from the center to any point on the circle.
Example: From K to H, or K to I, or K to J, or K to L.
✔ Answer: KH (or KI, KJ, KL)

#### c) Chord:
A chord is a segment whose endpoints lie on the circle.
Examples: HI, JL, HL, etc.
✔ Answer: HI (or any chord connecting two points on the circle)

#### d) Diameter:
A diameter is a chord that passes through the center. It’s the longest chord.
In the diagram, JL goes through the center K, so it's a diameter.
✔ Answer: JL

#### e) Secant:
A secant is a line that intersects the circle at two points.
Line GH passes through G and H (both on the circle), so it's a secant.
✔ Answer: GH

#### f) Tangent:
A tangent is a line that touches the circle at exactly one point.
Line GJ appears to touch the circle only at J, so it's a tangent.
✔ Answer: GJ

#### g) Point of Tangency:
This is the point where the tangent touches the circle.
Since GJ is tangent at J, the point of tangency is J.
✔ Answer: J

#### h) Minor Arc:
An arc less than 180°. For example, arc HI (from H to I along the shorter path).
✔ Answer: arc HI

#### i) Major Arc:
An arc greater than 180°. For example, arc HJI (going the long way around).
✔ Answer: arc HJI (or any arc that goes more than half the circle)

#### j) Semicircle:
An arc that is exactly 180°, formed by a diameter.
Since JL is a diameter, the semicircle is from J to L through either H or I.
✔ Answer: arc JHL or arc JIL (either half of the circle)

#### k) Central Angle:
An angle whose vertex is at the center (K) and sides are radii.
For example, ∠HKI or ∠JKL.
✔ Answer: ∠HKI

#### l) Inscribed Angle:
An angle whose vertex is on the circle and sides are chords.
For example, ∠HJI — vertex at J, sides JH and JI.
✔ Answer: ∠HJI

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✔ Answers for Problem 1:

| Letter | Answer |
|--------|--------|
| a) Center | K |
| b) Radius | KH |
| c) Chord | HI |
| d) Diameter | JL |
| e) Secant | GH |
| f) Tangent | GJ |
| g) Point of Tangency | J |
| h) Minor Arc | arc HI |
| i) Major Arc | arc HJI |
| j) Semicircle | arc JHL |
| k) Central Angle | ∠HKI |
| l) Inscribed Angle | ∠HJI |

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

Diagram shows:
- Circle with center J
- Points: G, H, M, L
- Line GH through the circle → secant
- Line MN touching at M → tangent
- Point M on circle, line NM tangent → point of tangency = M
- Segment MH → from M to H
- Segment MJ → from M to center J

Now match:

2. GH → A line passing through the circle at two points → Secant
✔ F. Secant

3. M → Point where tangent touches the circle → Point of tangency
✔ E. Point of tangency

4. MJ → Segment from point M on circle to center J → Radius
✔ D. Radius

5. J → The center of the circle → Center
✔ A. Center

6. MH → Segment from M to H, both on the circle → Chord
✔ B. Chord

7. GH → This is a ray/line going through the circle → Secant
✔ F. Secant (same as #2)

Wait — but note: GH appears twice? Actually, problem says:

> 7. $\overrightarrow{GH}$ → This is a ray starting at G going through H, which is a secant line.

So both 2 and 7 refer to GH, but 2 is just "GH" (segment), 7 is $\overrightarrow{GH}$ (ray).

But since both pass through the circle at two points, they are still secants.

✔ So both 2 and 7 → F. Secant

But let's check if there's a typo — likely GH is the same line.

So:

| Number | Term | Match |
|--------|------|-------|
| 2. GH | F. Secant |
| 3. M | E. Point of tangency |
| 4. MJ | D. Radius |
| 5. J | A. Center |
| 6. MH | B. Chord |
| 7. $\overrightarrow{GH}$ | F. Secant |

✔ Final Matching:
- 2 → F
- 3 → E
- 4 → D
- 5 → A
- 6 → B
- 7 → F

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Identifying Terms: Name the term that best describes the given line, segment, or point.

New diagram: Circle with center A, points: C, D, E, F, G, H, B

Let’s analyze:

21. CD → Segment from C to D, both on circle → Chord

22. FG → Line from F to G, passing through circle at E and H → goes through circle at two points → Secant

23. EC → From E to C, both on circle → Chord

24. AB → From center A to point B on circle → Radius

25. H → Point on the circle → Point on the circle
But what kind? H is where line FG touches the circle — is it a point of tangency?

Wait: FG is a secant, not tangent, because it crosses the circle at two points (E and H). So H is not a point of tangency.
It's just a point on the circle.

But maybe we're supposed to name its role.

But the question says: "Name the term that best describes the given line, segment, or point."

So:

- H is a point on the circle → but that's not a standard term.
But look: H lies on the circle, and it's also on a secant line.

But perhaps it's meant to be point of intersection or just point on the circle.

But among standard terms, H is just a point on the circle.

But wait — let’s check the options. There are no choices here — we must name the term.

Alternatively, perhaps H is a point of tangency? But no, FG is a secant, not tangent.

Unless... is FG tangent?

Wait: FG starts outside, goes through E and H — two points — so it's a secant.

So H is just a point on the circle.

But maybe the intended answer is point on the circle or endpoint of a chord.

But likely, H is just a point on the circle.

But let’s see:

26. A → Center of the circle → Center

So:

21. CD → Chord
22. FG → Secant
23. EC → Chord
24. AB → Radius
25. H → Point on the circle (but not special) — or perhaps point of intersection?
But standard term: point on the circle

Wait — maybe H is the point of tangency? But no, FG is a secant.

Unless the diagram shows something else...

Looking again:
- Line FG goes through E and H → two points → secant
- So H is just a point on the circle

But perhaps H is the point of tangency of another line? No, only FG is shown.

Wait — maybe H is the endpoint of a tangent? But no tangent is drawn.

So likely, H is just a point on the circle.

But in many worksheets, such a point is called simply a point on the circle.

But perhaps the answer is point on the circle.

But let’s recheck:

25. H → Since H is on the circle, and not specified otherwise, the best term is point on the circle.

But maybe it's point of intersection?

But “point of intersection” is vague.

Alternatively, if H is where the secant meets the circle, it’s a point of intersection.

But standard term: point on the circle.

However, in some contexts, H might be considered a vertex of an inscribed angle, but no angle is shown.

So safest: H is a point on the circle

But let’s see if the diagram has anything else.

Wait — H is on the circle, and line FG passes through it. So it's a point of intersection between the secant and the circle.

But the most accurate general term is point on the circle.

But perhaps the expected answer is point on the circle.

26. A → clearly the center

So:

| Question | Answer |
|---------|--------|
| 21. CD | Chord |
| 22. FG | Secant |
| 23. EC | Chord |
| 24. AB | Radius |
| 25. H | Point on the circle |
| 26. A | Center |

But sometimes H could be misidentified — let’s double-check.

Wait — H is on the circle, and FG is a secant, so H is a point of intersection.

But “point of intersection” is not a standard named part like “point of tangency”.

So better: point on the circle

Alternatively, if the question expects a specific term, maybe endpoint of a chord?

But H is an endpoint of EH, which is part of the secant.

But EH is not labeled.

So probably: point on the circle

But let’s assume standard answers.

Alternatively, in some textbooks, H might be called a point of contact — but only if tangent.

So unless it’s tangent, no.

So final answers:

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✔ Final Answers:

#### Problem 1:
a) Center: K
b) Radius: KH
c) Chord: HI
d) Diameter: JL
e) Secant: GH
f) Tangent: GJ
g) Point of Tangency: J
h) Minor Arc: arc HI
i) Major Arc: arc HJI
j) Semicircle: arc JHL
k) Central Angle: ∠HKI
l) Inscribed Angle: ∠HJI

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#### Problem 2: Match
2. GH → F. Secant
3. M → E. Point of tangency
4. MJ → D. Radius
5. J → A. Center
6. MH → B. Chord
7. $\overrightarrow{GH}$ → F. Secant

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#### Identifying Terms:
21. CD → Chord
22. FG → Secant
23. EC → Chord
24. AB → Radius
25. H → Point on the circle
26. A → Center

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✔ Note: If the worksheet has predefined choices, make sure to use those. But based on geometry definitions, these are correct.

Let me know if you'd like a diagram explanation!