All Things Circles

Dr. Tom Giles

All Things Circles

​REVIEW!!!

Vocabulary

​Circle	​
Arc​	Major arc​
Central Angle​	Minor arc​
Chord​	Point of tangency​
Circumference​	Radian measure​
Diameter​	Radius​
Inscribed angle​	Secant​
Intercepted arc​	Tangent segment​

​

Segments of a circle

Angles and arcs of a circle

Fill in the Blank

A _________ is the set of all points that are equidistant from another single point called the center.

Multiple Choice

It is the distance across the circle that passes through the center

• Radius

• Diameter

• Circumference

• Chord

​Circumference

​The circumference of a circle is the distance around the circle.

​

​

If you imagine the circle as a piece of string, it is the length of the string.

​

Multiple Choice

Which is true of a minor arc?

• It forms half a circle.
• It forms a whole circle.
• It measures greater than 180 degrees. 
• It measures less than 180 degrees.

Multiple Choice

Which is true of a major arc?

• Forms half a circle.
• Forms a whole circle.
• Measures greater than 180 degrees.
• Measures less than 180 degrees.

Multiple Choice

Which of the following would be a major arc in the diagram?

• BC
• BCD
• CD
• AB

Multiple Choice

Name a minor arc

• AD
• ADB
• AB
• CD

Multiple Choice

Name a semicircle.

• AD
• ABC
• BA
• BCA

Multiple Choice

What type of arc is arc AE?

• Major
• Minor
• Semi-circle
• Noah's

Multiple Choice

What type of arc is arc ABD?

• Major
• Minor
• Semi-circle
• Diameter

Multiple Choice

What type of arc is arc EC?

• Major
• Minor
• Semi-circle
• Radius

Multiple Choice

What type of arc is arc NMQ?

• Major
• Minor
• Semi-circle
• Sector

Multiple Choice

What type of arc is arc DGA?

• Major
• Minor
• Semi-circle
• Diameter

Multiple Choice

Correctly name a minor arc.

• arc AEC

• arc ADE

• arc AB

• arc AC

Central Angle

• A central angle of a circle has a vertex at the center and is formed by two radii.

Multiple Choice

What is this called?

• Radius

• Central Angle

• Major Arc

• Inscribed Angle

Multiple Choice

What is this called?

• Tangent Line

• Central Angle

• Chord

• Inscribed Angle

​Time to practice all of your words!

• Center Point

• ​radius

• ​chord

• ​diameter

• ​tangent line

• ​point of tangency

• ​secant line

• Circumference

• ​major arc

• ​minor arc

• ​semicircle

• ​central angle

• ​inscribed angle

Multiple Choice

What is this called?

• Chord

• Minor arc

• Secant

• Diameter

Multiple Choice

What is this called?

• Radius

• Central Angle

• Major Arc

• Inscribed Angle

Multiple Choice

What is this called?

• Tangent Line

• Secant

• Chord

• Diameter

Multiple Choice

What is this called?

• Tangent Line

• Central Angle

• Chord

• Inscribed Angle

Multiple Choice

What is this called?

• Circumference

• Minor Arc

• Major Arc

• Inscribed Angle

Multiple Choice

What is this called?

• Circumference

• Minor Arc

• Major Arc

• Inscribed Angle

Multiple Choice

What is this called?

• Major Arc

• Minor Arc

• Circumference

• Perimeter

Multiple Choice

A segment with 2 endpoints on the circle.

• Chord
• Diameter
• Radius
• Inscribed Angle

Multiple Choice

This is a picture of ___________.

• Chord
• Diameter
• Radius
• Inscribed Angle

Multiple Choice

This is a picture of ___________.

• Chord

• Diameter

• Radius

• Inscribed Angle

Multiple Choice

A segment that goes from edge to edge through the center.

• diameter

• radius

• tangent

• chord

Multiple Choice

A line that touches the circle only once.

• diameter

• radius

• tangent

• chord

Multiple Choice

A line that goes through a circle intersecting the circle at two points.

• diameter

• chord

• tangent

• secant

Multiple Choice

The perimeter of a circle is called...

• circumference

• arc

• radius

• tangent

Multiple Choice

A piece of the circumference is called...

• radius

• diameter

• arc

• tangent

Multiple Choice

This is a picture of ___________.

• Minor Arc

• Major Arc

• Semi-Circle

• Central Angle

Multiple Choice

This is a picture of ___________angle.

• Major Arc

• Minor Arc

• Central Angle

• Inscribed Angle

Multiple Choice

This is a picture of ___________ angle.

• Major Arc

• Minor Arc

• Central Angle

• Inscribed Angle

Measurements of Arc Length in Circles

Arcs: Part of a Circle

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

The radius of a circle is 4 feet. What is the EXACT length of a 

$$225\degree$$  arc?

• 10 pi

• 225

• 2.5 pi

• 5 pi

​arc length=5pi

(in calculator you can type in the numbers and then add pi to your answer)​

​EXACT length left in terms of pi

​Set Up your proportion:

​Finding EXACT Length of Arc

Some text here about the topic of discussion

Multiple Choice

When the dog is outside she is tied to a stake in the center of a circular area of radius 24 feet. The angle between her dog house and her favorite hydrant is 165 degrees. What is the length of the arc from her dog house to the hydrant, following minor arc DG, to the nearest foot.

• 40

• 35

• 55

• 69

​When finding arc length that isn't in terms of pi...

Substitute ​3.14 for the pi symbol into your proportion or use the pi key on the calculator. You will more than likely get a decimal answer that you will need to round according to the specifications of the problem.

Geometry​

Arc Length​

Multiple Choice

what is the arc length

• 5.23
• 103
• 33.33
• 50

Multiple Choice

The arc length is 7cm

• True

• False it's 6.8cm

• False it's 7.4 cm

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

Multiple Choice

The radius of a circle is 7 feet. What is the approximate length of an 85 degree arc?

• 3.31 feet

• 14.83 feet

• 5.19 feet

• 10.39 feet

Fill in the Blank

A circle has a radius of 3. A central angle is created with a measure of 40 degrees. Find the length of the arc created by this central angle to two decimal places.

Multiple Choice

Find the arc length.  Leave your answer in terms of π.

• 7/4π
• 7/2π
• 1/8π
• 45π

Fill in the Blank

Find the EXACT length of a 60 degree arc that is in a circle with a radius of 6 feet. 

(type pi instead of using symbol

$$\pi$$  )

Fill in the Blank

What is the EXACT length of the 90 degree arc in the figure?

(Type in pi instead of symbol)