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Warm up

Warm up. This will be graded in 10 minutes. 21 30° 6. 100°. 150° 3 3. 40°. Today’s agenda. Turn-in Chap 6 notes Make a notebook 9.1 notes and discussion Assignment: Pg 570 11-43. Notice the notation for a circle. It’s named by the center point.

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Warm up

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  1. Warm up • This will be graded in 10 minutes. • 21 • 30° • 6. 100° • 150° • 3 • 3. 40°

  2. Today’s agenda Turn-in Chap 6 notes Make a notebook 9.1 notes and discussion Assignment: Pg 570 11-43

  3. Notice the notation for a circle. It’s named by the center point. The center point is also known as the vertex of the circle. 9.1 Chords and Arcs Some important parts of a circle: A chord is a segment that touches either side of a circle The diameter of a circle is a chord that goes through the center of the circle. The radius of a circle is a segment that touches the center of the circle and the side.

  4. Arc Notation and Description • A minor arc is labeled with 2 capital letters which are the endpoints and measures less than 180°. • Major arcs and semicircles are labeled with 3 letters – the endpoints and any ONE point in between. • Semicircle = 180° • Major arc is greater than 180°

  5. Degree Measures of Arcs • A central angle is formed by the intersection of 2 segments at the center of a circle. • The endpoints of the segment that intersect the edge of the circle are the endpoints of the intercepted arc.

  6. Arcs can be measured in terms of degrees. • The degree measure of a minor arc is the measure of its central angle. • The degree measure of a major arc is 360° minus the degree measure of its minor arc. (In this case the major arc ACB would be 360°-85° = 275°) • The degree measure of a semicircle is 180°. C

  7. Arc Length • A second way to measure an arc is in terms of its length. • arc Length = the degree Measure of an arc (the circumference of the circle) 360° L = M (2πr) 360° Find the length of arc AB if segment AX = 10 units. L = 85 (2 π 10) = 14.83 in. 360 X

  8. Let’s Practice • Degree measure of arc AB = • Degree measure of arc CA = • Degree measure of arc BC = • Degree measure of arc BAC = • Length of arc AB = 70° 130° 160° 200° 3.66 units

  9. WHITEBOARDS!! Determine the length of an arc with the given central angle measure, mP, in a circle with radius r. Round to the nearest hundredth. • m P = 40°; r = 6 • m P = 75°; r = 20 • m P = 80°; r = 39 • m P = 130°; r = 61 4.19 26.18 54.45 138.4

  10. Let’s switch gears Determine the degree measure of an arc with the given length, L, in a circle with radius r. • L = 52; r = 14 • L = 35; r = 11 • L = 8; r = 2 • L = 27; r = 5 212.8 ° 182.3° 229.2° 309.4°

  11. Quick Review • What is a radius of a circle? • What is a chord of a circle? • What is the diameter of a circle? • Is the diameter of a circle a chord? • What is the notation for a minor arc? • What is the notation for a major arc? • What is a semicircle? • What is the notation for a semicircle? • What is the notation for ‘circle P’? • What is an intercepted arc? • What is a central angle? • If a central angle is 43° what is the measure of the intercepted arc? • What are the two ways arcs can be measured. • What is the formula for Arc Length?

  12. Your assignment Pg 570 11-43

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