1. Circles
3/30/09

2. Circle
Definition
A circle is the set of all points in a plane that are equidistant from a given point in the plane known as the center of the circle.
How do we represent
a circle

3. Parts of A Circle Radius
A segment from the center of the circle to a point on the circle.

4. What can we say about all the radii of a circle?
They are all equal! 8

5. Parts of a Circle
CHORD
Is a segment whose endpoints lie on a circle.

6. Parts of a Circle Diameter
Is a chord that contains the center of a circle.

7. Diameter/Radius
What do we know about the radius of a circle and its diameter?
The diameter is TWICE the radius.

8. Parts of a Circle Arc Endpoints An unbroken part of a circle.
Any two distinct points on a circle divide the circle into two arcs.
Endpoints
The two distinct points of the arcs

9. Parts of a Circle Semicircle
An arc whose endpoints are endpoints of a diameter.
Also known as a “half-circle”

10. Parts of a Circle Minor Arc Major Arc
Is an arc that is shorter than a semicircle of that circle
Major Arc
Is an arc that is longer than a semicircle of that circle.

11. Parts of a Circle Central Angle
It is an angle whose vertex is the center of the circle.

12. Degree Measures of Arcs
The degree measure of a MINOR ARC is the measure of its central angle.

13. Degree Measures of Arcs
The degree measure of a major arc is 360o minus the degree measure of its minor arc.

14. Degree Measures of Arcs

15. Degree Measures of Arcs
The degree measure of a semicircle is 180o

16. Arc Length
If r is the radius of a circle and M is the degree measure of an arc of the circle, then the length, L, of the arc is given by the following:

20. Class Work WS
9.1

21. Homework
Page 570
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