Warm up

♥ This will be graded in 10 minutes.4. 21

5. 30°

6. 100°

1. 150°

2. 3

3. 40°

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 ArcsSome 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.

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.

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, mP, in a circle with radius r. Round to the nearest hundredth.

1. m P = 40°; r = 62. m P = 75°; r = 203. m P = 80°; r = 394. m P = 130°; r = 61

4.1926.1854.45138.4

Let’s switch gears

Determine the degree measure of an arc with the given length, L, in a circle with radius r.

1. L = 52; r = 142. L = 35; r = 113. L = 8; r = 24. L = 27; r = 5

212.8 °182.3°229.2°309.4°

Quick Review1) What is a radius of a circle?2) What is a chord of a circle?3) What is the diameter of a circle?4) Is the diameter of a circle a chord?5) What is the notation for a minor arc?6) What is the notation for a major arc?7) What is a semicircle?8) What is the notation for a semicircle?9) What is the notation for ‘circle P’?10)What is an intercepted arc?11)What is a central angle?12)If a central angle is 43° what is the measure of the

intercepted arc?13)What are the two ways arcs can be measured.14)What is the formula for Arc Length?

Your assignment

Pg 570

11-43