True or False: Is the Radius of a Circle a Chord?

Circle Terminology with Definition Distinctions

True or false:

The radius of a circle is the chord.

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Step-by-step written solution

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1

Understand the problem

True or false:

The radius of a circle is the chord.

2

Step-by-step solution

To solve this question, we must understand the definitions of the terms "radius" and "chord" in the context of a circle:

  • A radius is a line segment that connects the center of the circle to any point on the circle's circumference. All radii of a circle are equal in length.
  • A chord is a line segment whose endpoints both lie on the circle's circumference. The chord does not necessarily pass through the center of the circle, and chords can have different lengths.

Given these definitions, observe the following points:

  • The radius is inherently different from the general concept of a chord because the radius must include the circle's center as one of its points, while a chord only specifies that both endpoints lie on the circle's edge, offering no requirement to pass through the center.
  • An important sub-case is the diameter, which is a special chord that does pass through the center and is equal to twice the radius (2r2r). However, while the diameter is indeed a chord, the radius itself cannot be viewed as such because it does not completely lie between two points on the circle but instead starts from the center.

Hence, the statement that "The radius of a circle is the chord" is false because a radius does not fulfill the general definition of a chord, which requires two endpoints on the circle's circumference that do not include the center of the circle.

Therefore, the correct choice is False.

3

Final Answer

False

Key Points to Remember

Essential concepts to master this topic
  • Definition: Radius connects center to circumference, chord connects circumference to circumference
  • Technique: Check endpoints - radius has center + edge point, chord has two edge points
  • Check: Diameter is special chord with length 2r 2r , but radius ≠ chord ✓

Common Mistakes

Avoid these frequent errors
  • Confusing radius with diameter as chords
    Don't think radius is a chord because it touches the circle = wrong classification! A radius has one endpoint at the center, not on the circumference like chords require. Always check that both endpoints of a chord lie on the circle's edge.

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 radius and chord?

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A radius goes from the center to the edge of the circle, while a chord connects two points on the edge. Think of it like this: radius has one foot in the 'middle', chord has both feet on the 'rim'!

Is the diameter considered a chord?

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Yes! The diameter is a special chord that passes through the center. It's the longest possible chord in any circle, with length 2r 2r .

Can a chord be longer than the radius?

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Absolutely! Most chords are longer than the radius. The diameter (the longest chord) is always twice the radius length. Only very small chords near the edge might be shorter than the radius.

Why isn't radius a chord if it touches the circle?

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Because a chord needs both endpoints on the circumference. The radius has one endpoint at the center and one on the circumference, so it doesn't meet the chord definition.

How can I remember the difference?

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Think of Radius as 'Reach' from center to edge, and Chord as 'Connecting' two edge points. This way you'll never mix them up!

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