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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
• 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.

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.

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
• 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.
• 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
• 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
• 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!!

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

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
• 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

Pg 570

11-43