Geometry Chapter 10 Parts of a Circle Worksheet 12, Give an example of each circle part using the diagram below:, a) Center: b) Radius: Chord; Diameter; 2) Secant; Tangent: 9) Point of Tangency:, h) ... - Free Printable

Let's solve the problem step by step using the diagram and the worksheet provided.

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

We are given a circle with labeled points:
- Points on the circle: $ J, I, L, H $
- Center: $ K $
- External point: $ G $
- Lines: $ GH $, $ GI $, $ JL $, $ KI $, $ KJ $, etc.

Let’s go through each part:

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

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#### b) Radius:
A radius is a segment from the center to any point on the circle.
Examples: $ KJ $, $ KI $, $ KL $, $ KH $
✔ Answer: $ KJ $ (or any of the others)

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#### c) Chord:
A chord is a segment whose endpoints lie on the circle.
Examples: $ JL $, $ HI $, $ IL $, etc.
✔ Answer: $ JL $

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#### d) Diameter:
A diameter is a chord that passes through the center. It is twice the length of the radius.
In the diagram, $ JL $ does not pass through $ K $, but $ IL $ or $ HI $ might not either. Wait — look carefully.

Actually, there is no clear diameter shown unless one of the chords goes through the center.

But we see that $ K $ is the center, and if $ I $ and $ L $ are endpoints of a line passing through $ K $, then $ IL $ would be a diameter.

Wait — in the diagram, $ K $ lies on segment $ IL $? Yes, since $ K $ is the center and $ I $ and $ L $ are on the circle, and $ K $ is between them — so $ IL $ is a diameter.

✔ Answer: $ IL $

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#### e) Secant:
A secant is a line that intersects the circle at two points.
Line $ GH $ intersects the circle at $ H $ and $ J $. So $ GH $ is a secant.
✔ Answer: $ GH $

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#### f) Tangent:
A tangent is a line that touches the circle at exactly one point.
Line $ GJ $ touches the circle only at $ J $.
✔ Answer: $ GJ $

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#### 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 $

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#### h) Minor Arc:
A minor arc is an arc less than 180°.
Example: $ \overset{\frown}{JL} $, $ \overset{\frown}{JI} $, $ \overset{\frown}{HL} $, etc.
✔ Answer: $ \overset{\frown}{JL} $

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#### i) Major Arc:
A major arc is greater than 180°. We denote it with three letters.
Example: $ \overset{\frown}{JIL} $, $ \overset{\frown}{HJL} $, etc.
✔ Answer: $ \overset{\frown}{JIL} $

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#### j) Semicircle:
A semicircle is an arc that is exactly half the circle (180°), formed by a diameter.
Since $ IL $ is a diameter, the arcs $ \overset{\frown}{IHL} $ or $ \overset{\frown}{IJL} $ could be semicircles. But we need to check which one is defined.

If $ IL $ is the diameter, then the semicircle could be $ \overset{\frown}{IHL} $ or $ \overset{\frown}{IJL} $. Since $ J $ and $ H $ are on the circle, and $ IL $ is the diameter, both arcs from $ I $ to $ L $ via $ J $ or $ H $ are semicircles.

But typically, we name it with three points. Let's assume $ \overset{\frown}{IJL} $ is the semicircle.

✔ Answer: $ \overset{\frown}{IJL} $ (or $ \overset{\frown}{IHL} $)

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#### k) Central Angle:
A central angle has its vertex at the center and sides passing through two points on the circle.
Example: $ \angle IKJ $, $ \angle LKJ $, $ \angle HKJ $, etc.
✔ Answer: $ \angle IKJ $ (or any central angle)

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#### l) Inscribed Angle:
An inscribed angle has its vertex on the circle and sides intersecting the circle.
Example: $ \angle IJL $ — vertex at $ J $, on the circle, and sides $ JI $ and $ JL $ going to other points on the circle.

✔ Answer: $ \angle IJL $

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✔ Final Answers for Part 1:

| Letter | Answer |
|--------|--------|
| a) Center | $ K $ |
| b) Radius | $ KJ $ |
| c) Chord | $ JL $ |
| d) Diameter | $ IL $ |
| e) Secant | $ GH $ |
| f) Tangent | $ GJ $ |
| g) Point of Tangency | $ J $ |
| h) Minor Arc | $ \overset{\frown}{JL} $ |
| i) Major Arc | $ \overset{\frown}{JIL} $ |
| j) Semicircle | $ \overset{\frown}{IJL} $ |
| k) Central Angle | $ \angle IKJ $ |
| l) Inscribed Angle | $ \angle IJL $ |

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

> 2. GH
From earlier, $ GH $ is a secant because it intersects the circle at two points: $ H $ and $ J $.
So, GH → Secant

But the options are:
- A. Center
- B. Chord

Wait — this seems incomplete. The matching list only shows A and B, but we need more options.

Looking at the image:
It says:
2. GH
3. M

And choices:
A. Center
B. Chord

But “M” is not labeled in the diagram above — perhaps there’s a typo or missing image.

However, based on what we have:

- $ GH $ is a secant, not a chord (since it extends beyond the circle).
- But chord is only a segment *within* the circle.

So $ GH $ is not a chord; it's a secant.

But if only "Chord" is listed as an option, maybe they expect $ GH $ to be matched with something else?

Wait — perhaps the second diagram is different.

But in your image, below the first question, it says:

> Match the part of the circle with the term that best describes it.
> 2. GH
> 3. M
> A. Center
> B. Chord

But “M” is not visible in the diagram. Also, no other labels like “Center” or “Chord” are clearly marked.

Possibility: In the second diagram (which is partially cut off), there may be a point labeled $ M $, and $ GH $ is a line.

But from what we can see:
- $ GH $ is a straight line passing through the circle at $ H $ and $ J $ → secant
- But “secant” is not among the choices.
- “Chord” is a segment between two points on the circle, so $ HJ $ would be a chord, not $ GH $

So likely, GH should be matched with Secant, but it's not listed.

Unless the options are not fully shown.

Alternatively, maybe the question is asking to match:

- GH → Secant (but not listed)
- M → ? (maybe the center?)

But without seeing the full second diagram, we can't be certain.

However, based on standard geometry:

- $ GH $: Secant
- If $ M $ is the center, then $ M $ → Center

But again, $ M $ is not visible in the current diagram.

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✔ Conclusion:

For Part 1, the answers are filled correctly as per the diagram.

For Part 2, assuming the options are limited:

- 2. GH → Secant (but not listed; possibly a typo)
- 3. M → Center (if M is the center)

But since the options are only:
- A. Center
- B. Chord

Then:
- If $ M $ is the center → A. Center
- If $ GH $ is a chord? No, it's a secant, not a chord.

So unless $ GH $ refers to the segment *inside* the circle ($ HJ $), but it's labeled $ GH $, which includes external part.

Therefore, likely:
- $ GH $ → Secant (but not in options)
- $ M $ → Center → A

But without full context, we can’t complete Part 2 confidently.

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✔ Final Answer Summary:

#### Part 1:
a) $ K $
b) $ KJ $
c) $ JL $
d) $ IL $
e) $ GH $
f) $ GJ $
g) $ J $
h) $ \overset{\frown}{JL} $
i) $ \overset{\frown}{JIL} $
j) $ \overset{\frown}{IJL} $
k) $ \angle IKJ $
l) $ \angle IJL $

#### Part 2 (partial):
- 2. GH → Secant (not in given options)
- 3. M → A. Center (assuming M is the center)

Please verify the second diagram if possible.