Understanding Chords: Connecting Two Points on a Circle's Circumference

Circle Geometry with Basic Chord Definition

A chord is a segment that connects two points on a circle.

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

A chord is a segment that connects two points on a circle.

2

Step-by-step solution

To determine the truth of the statement, we must consider the precise definition of a chord in the context of circle geometry:

A chord is specifically defined as a line segment whose endpoints both lie on a circle. This segment connects two distinct points on the circumference of the circle. This definition highlights the role of the chord as a geometric entity within the circle.

Given this definition, we evaluate the statement: "A chord is a segment that connects two points on a circle."

The provided statement accurately describes the nature of a chord. The endpoints of the segment must be on the circle, thus aligning perfectly with the standard definition of a chord.

Therefore, the statement is True.

3

Final Answer

True

Key Points to Remember

Essential concepts to master this topic
  • Definition: A chord connects two points on a circle's circumference
  • Identification: Both endpoints must lie exactly on the circle boundary
  • Verification: Check that segment endpoints touch the circle's edge ✓

Common Mistakes

Avoid these frequent errors
  • Confusing chords with other circle segments
    Don't think any line touching a circle is a chord = wrong identification! A chord specifically needs both endpoints ON the circle, not just touching it. Always ensure both endpoints lie exactly on the circumference.

Practice Quiz

Test your knowledge with interactive questions

M is the center of the circle.

Perhaps \( MF=MC \)

MMMAAABBBCCCDDDEEEFFFGGGHHH

FAQ

Everything you need to know about this question

What's the difference between a chord and a diameter?

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A diameter is a special type of chord that passes through the center of the circle. All diameters are chords, but not all chords are diameters!

Can a chord be outside the circle?

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No! A chord must have both endpoints on the circle. If any part extends outside, it's not a chord but a different type of line segment.

Is a chord the same as a radius?

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Not at all! A radius goes from the center to one point on the circle, while a chord connects two points on the circumference without necessarily touching the center.

What's the shortest possible chord?

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Technically, there's no shortest chord since you can make them infinitely small. However, the longest chord is always the diameter!

How do I know if two points make a chord?

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Simply check: Are both points on the circle's edge? If yes, then the line segment connecting them is definitely a chord.

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