Dorchester2 - 03-04-2025-Arc Length and Area of Sectors

​Take out your notes!

Open Ended

Can you move these matches and change the number to sixteen?

How many moves are needed?

Be prepared to explain your reasoning to the class.

Open Ended

Click on the image.

● I can define the parts of a circle
● I can define and measure in a circle
● I can find the measure of segments of a circle
● I can discover the properties of tangent lines
● I can find the measure of angles inside and outside of a circle
● I can find missing measures of angles and arcs using circle theorems.

● I can explain radian angle measures in terms of a circular radius and
arc length

Objectives

Circle Vocab

Draw

Line AB is tangent to circle O. 

Segment AF is a diameter.  The measure of arc AG = 100°.

The measure of arc CE = 30°.

The measure of arc m EF = 25°. 

Draw the given information on the circle.

Use the given information and circle theorems to find the measure of < 1.

Draw

Line AB is tangent to circle O. 

Segment AF is a diameter. 

The measure of arc AG = 100°.

The measure of arc CE = 30°.

The measure of arc m EF = 25°. 

Draw the given information on the circle.

Use the given information and circle theorems to find the measure of < 3.

Draw

Line AB is tangent to circle O. 

Segment AF is a diameter. 

The measure of arc AG = 100°.

The measure of arc CE = 30°.

The measure of arc m EF = 25°. 

Draw the given information on the circle.

Use the given information and circle theorems to find the measure of < 6.

Draw

Line AB is tangent to circle O. 

Segment AF is a diameter. 

The measure of arc AG = 100°.

The measure of arc CE = 30°.

The measure of arc m EF = 25°. 

Draw the given information on the circle.

Use the given information and circle theorems to find the measure of < 7.

Draw

Line AB is tangent to circle O. 

Segment AF is a diameter. 

The measure of arc AG = 100°.

The measure of arc CE = 30°.

The measure of arc m EF = 25°. 

Draw the given information on the circle.

Use the given information and circle theorems to find the measure of < 8.

Draw

Find the measure of x.

Show your process.

Segment Lengths

​https://youtu.be/aCdMntchnl0?feature=shared

Draw

Find x.

Show your process. Round to the nearest tenth.

Draw

Find x.

Show your process.

More about Arcs

https://study.com/academy/lesson/measure-of-an-arc.html

Arcs of a Circle

• Minor Arc

• Major Arc

• Semicircle

Adjacent Arcs vs. Non-Adjacent Arcs

​The measure of an arc is the degree of the angle that intercepts the arc. Remember that the measure of an arc is a degree, not a distance.
https://study.com/academy/lesson/measure-of-an-arc.html

​Arc length is literally the length of the arc of a portion of a circle.
This arc is a part of the total circumference of a circle.
This length is measured as a linear distance.

https://study.com/academy/lesson/arc-length-definition-equation.html

Multiple Choice

Which proportion set up correctly for the figure?

• $$\frac{arc\ length}{8\pi}=\frac{225\degree}{360\degree}$$

• $$\frac{arc\ length}{4\pi}=\frac{225\degree}{360\degree}$$

• $$\frac{arc\ length}{16\pi}=\frac{225\degree}{360\degree}$$

• $$\frac{arc\ length}{8\pi}=\frac{360\degree}{225\degree}$$

Multiple Choice

Which proportion is set up correctly for the figure?

• $$\frac{arc\ length}{8\pi}=\frac{180\degree}{360\degree}$$

• $$\frac{arc\ length}{4\pi}=\frac{180\degree}{360\degree}$$

• $$\frac{arc\ length}{16\pi}=\frac{180\degree}{360\degree}$$

• $$\frac{arc\ length}{360\degree}=\frac{4\pi}{180\degree}$$

Multiple Choice

what is the arc length

• 5.23
• 103
• 33.33
• 50

Multiple Choice

If an exact arc length is

$$\frac{4\pi}{7}$$  , approximate the length to the nearest hundedth. 

• 12.56

• 1.80

• 1.74

• 1.71

​https://study.com/academy/lesson/finding-the-area-of-a-sector-formula-practice-problems.html

Central Angle

• Central angles are angles with a vertex at the center of the circle.

• Arcs are pieces of a circle's border. (crust of pizza/pie)

• The measure of a central angle is equal to the measure of its intercepted arc.

Draw

Use what you know about circles vocabulary and theorems to solve for the missing angle.

 Line AB is tangent to circle O. 

Segment AF is a diameter. 

The measure of arc AG = 100°.

The measure of arc CE = 30°.

The measure of arc EF = 25°.

Find the measure of angle 1.