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Circles

Circles. 3/30/09. 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. Parts of A Circle. Radius

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Circles

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  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 TWICEthe radius.

  8. Parts of a Circle • Arc • 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 • 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:

  17. Class Work • WS • 9.1

  18. Homework • Page 570 • 11-19

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