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.

• 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.
• ALL radii of one circle are the same length (congruent to each other).

Review

• Perimeter – the distance around the outside of a polygon

Notes

• 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 $\overline{AT}$

• 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.

• 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 $\odot{A}$.

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)