1. Circles

2. 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. 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. 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. 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. 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  r or C =  d.

21. 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 =  r 2

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(  r 2 )