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Chapter 11

Chapter 11. Circles. Section 11-1. Parts of a Circle. Circle. A circle is the set of all points in a plane that are a given distance from a given point in the plane, called the center of the circle. Segments of a Cirlce. Radius – has one endpoint on the center and one on the circle

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Chapter 11

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  1. Chapter 11 Circles

  2. Section 11-1 Parts of a Circle

  3. Circle • A circle is the set of all points in a plane that are a given distance from a given point in the plane, called the center of the circle.

  4. Segments of a Cirlce • Radius – has one endpoint on the center and one on the circle • Chord – has both endpoint on the circle • Diameter – a chord that passes through the center

  5. Theorem 11-1 • All radii of a circle are congruent.

  6. Theorem 11-2 • The measure of the diameter of a circle is twice the measure of the radius of the circle.

  7. Section 11-2 Arcs and Central Angles

  8. Types of Arcs • Minor Arc – measure is less than 180° • Major Arc – measure is greater than 180° • Semicircle – measure equals 180°

  9. Definition of Arc Measure • The degree measure of a minor arc is the degree measure of its central angle. • The degree measure of a major arc is 360 minus the degree measure of its central angle. • The degree measure of a semicircle is 180.

  10. Postulate 11-1 • The sum of the measures of two adjacent arcs is the measure of the arc formed by the adjacent arcs.

  11. Theorem 11-3 • In a circle or in congruent circles, two minor arcs are congruent if and only if their corresponding central angles are congruent.

  12. Section 11-3 Arcs and Chords

  13. Theorem 11-4 • In a circle or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

  14. Theorem 11-5 • In a circle, a diameter bisects a chord and its arc if and only if it is perpendicular to the chord.

  15. Section 11-4 Inscribed Polygons

  16. Inscribed Polygon • A polygon is inscribed in a circle if and only if every vertex of the polygon lies on the circle. • The circle is circumscribed about the polygon

  17. Theorem 11-6 • In a circle or in congruent circles, two chords are congruent if and only if they are equidistant from the center.

  18. Section 11-5 Circumference of a Circle

  19. Circumference • The distance around a circle

  20. Theorem 11-7 • If a circle has a circumference of C units and a radius of r units, then C= 2ror C = d.

  21. Section 11-6 Area of a Circle

  22. Theorem 11-8 • If a circle has an area of A square units and a radius of r units, then A = r2

  23. Theorem 11-9 • If a sector of a circle has an area of A square units, a central angle measurement of N degrees, and a radius of r units, then A = N/360(r2)

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