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6.1 – What is a Circle?

Key Terms

  • Center of the Circle – The point at the exact center of a circle.
    • All points on a circle are the same distance from the center.
    • The “middle” of the circle.
  • Circle – A geometric figure consisting of all the points on a plane that are the same distance from a single point (the center).
    • That distance is called the radius.
    • All of those points are on the edge of the circle.
    • The center is in the middle of the circle.
    • A circle is the collection of points in a plane that are the same distance from a given point in the plane.

GeoB 6.1 - Center

  • Circumference – The distance around a circle.
    • Measured using the radius or diameter: 2\pi r or \pi d
    • It’s similar to the idea of perimeter.
    • To get a rough estimate of a circle’s circumference, multiply its radius by 6.
      • Ex. Radius: 8, so instead of 2\pi 8, you can use (8 \cdot 6) to estimate.  C\approx 48.
        • This works because \pi \approx 3.14 and 2\pi \approx 6.28, so rounding down to 6 works for an estimate.
  • Radius – A line segment that has one endpoint at the center of a circle and the other endpoint anywhere ON the circle.
    • It is the segment that connects the center of the circle to the edge of the circle.
    • Radius also means “the length of such a line segment.”
    • The radius of a circle is half of its diameter.
    • The plural of radius is radii.
    • ALL radii of one circle are the same length (congruent to each other).

GeoB 6.1 - Radius

 


Review

  • Perimeter – the distance around the outside of a polygon

 


Notes

  • Radius
    • Size of the Circle
      • To increase the size of the circle, increase the length of the radius.
      • To decrease the size of the circle, decrease the length of the radius.
    • Circles have infinite number of radii
    • Radii are line segments from the center of the circle to the circle’s edge
      • Ex. The radii drawn in this circle are: \overline{AR}\overline{AP}\overline{AG}, and \overline{AT}

GeoB 6.1 Radii

 

  • Center
    • The center of a circle is named with a point using a capital letter.
      • Ex. This is circle S named for the circle’s center, S.

GeoB 6.1 Center

 

  • Notation
    • Circles are written with a small circle with a dot inside, then the letter of the center.
      • Ex. the image below is circle A, written as \odot{A}.

GeoB 6.1 Notation

 


Examples

  • Ex 1. What is the circumference of a circle with radius 5cm?
    • Formula: Circumference = 2πr
      • C=2π(5)
      • C=10π
      • C=31.4cm (rounded to about 31cm)

 


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