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

Today’s agenda

Turn-in Chap 6 notes

Make a notebook

9.1 notes and discussion

Assignment: Pg 570 11-43

9 1 chords and arcs

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.

slide4

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°
degree measures of arcs
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.
arcs can be measured in terms of degrees
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

arc length
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

let s practice
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

whiteboards
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

let s switch gears
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°

quick review
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?
your assignment
Your assignment

Pg 570

11-43