Circle Geometry: Identifying the Radius Among Given Segments

Circle Segments with Center Connection

Identify which diagram shows the radius of a circle:

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Understand the problem

Identify which diagram shows the radius of a circle:

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Step-by-step solution

Remember that a radius is a line segment connecting the center of the circle to a point that lies on the circle itself.

In drawing A, the line doesn't touch any point on the circle itself.

In drawing B, the line doesn't pass through the center of the circle.

We can see that in drawing C, the line that extends from the center of the circle is indeed connected to a point on the circle itself.

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Final Answer

Key Points to Remember

Essential concepts to master this topic
  • Definition: Radius connects circle center to any point on circumference
  • Identification: Look for line from center dot to circle edge
  • Verification: Both endpoints must touch center and circumference exactly ✓

Common Mistakes

Avoid these frequent errors
  • Confusing radius with any line inside the circle
    Don't assume any line segment in a circle is a radius = wrong identification! Lines that don't start at the center or don't reach the edge are chords, secants, or other segments. Always check that one endpoint is the center and the other is on the circumference.

Practice Quiz

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Where does a point need to be so that its distance from the center of the circle is the shortest?

FAQ

Everything you need to know about this question

How can I quickly identify the center of a circle?

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The center is usually marked with a dot or small circle. It's the point that's exactly the same distance from every point on the circle's edge.

What's the difference between radius and diameter?

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A radius goes from center to edge, while a diameter goes all the way across the circle through the center. The diameter is always twice as long as the radius!

Can a circle have more than one radius?

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Yes! A circle has infinitely many radii because you can draw a line from the center to any point on the circumference. They're all the same length though.

What if the line goes past the circle edge?

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If a line starts at the center but extends beyond the circle, the radius is only the part from center to where it first touches the edge. The rest doesn't count as radius.

Is a chord the same as a radius?

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No! A chord connects any two points on the circle's edge, while a radius must start at the center. Only diameters are chords that pass through the center.

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