Circles 1- Arc, Radians & Nomenclature

Circles 1- Parts, Arc & Radians

this lesson will define many terms specific to circles and relate angles formed by intersection of circles and lines

Circle Nomenclature

Tangent & Secant Lines

A Tangent is a Line that Intersects a Circle at exactly one point on the circle-called the point of Tangency

A Secant Line Goes through a circle, Intersecting it at exactly two points

Tangent

• not to be confused with the Trig Ratio

• The Tangent is a Line Perpendicular to a radius at the point of tangency

Secant

• not the trig ratio, this is a line

• A Secant "cuts across" a circle

• A Secant Line intersects a circle at exactly 2 points

Chords

A chord is the segment of a secant that is interior the circle and has endpoints on the circumference.

The Diameter is the longest Chord

Multiple Choice

Name the circle part shown in red

• Diameter

• Circumference

• Radius

• Perimeter

Multiple Choice

What is being represented (black) in the image?

• Diameter

• Chord

• Radius

• Concentric Circles

Multiple Choice

What is being represented (black) in the image?

• Radius

• Diameter

• Inscribed Angle

• Secant

Multiple Choice

The distance around the perimeter of a circle is called

• Circle

• Radius

• Diameter

• Circumference

Multiple Choice

What is being represented (green) in the image?

• Chords

• Tangents

• Exterior Angle

• Central Angle

Multiple Choice

What is being represented in the image?

• Tangent

• Concentric Circles

• Exterior Angle

• Secant

Multiple Choice

Name the circle part shaded in green

• Radius

• Diameter

• Semi-circle

• Arc

Multiple Choice

What is P?

• chord
• secant
• point of tangency
• tangent

Multiple Choice

What is line PT?

• chord
• secant
• point of tangency
• tangent

Multiple Choice

What is line AB?

• diameter
• chord
• secant
• tangent

Multiple Choice

What is O?

• diameter
• radius
• center
• chord

Multiple Choice

What is segment AB?

• diameter
• radius
• tangent
• chord

Multiple Choice

What is segment PQ?

• diameter
• radius
• tangent
• chord

Multiple Choice

What is segment OC?

• diameter
• radius
• tangent
• chord

Multiple Choice

The radius of a bowling ball is 4.25 inches. What is the diameter?

• 8.5 inches

• 4.25 inches

• 12.75 inches

Multiple Choice

The diameter of a soccer ball is 8.6 inches. What is the radius?

• 4.3 inches

• 8.6 inches

• 17.2 inches

Multiple Choice

The radius is ____ the diameter

• half

• double

• one third of

• bigger than

Multiple Choice

Which picture shows a tangent?

Multiple Choice

Which picture shows a chord?

Arc & Arc Length

Arc is Angle or Degree and is defined by the Central Angle

Arc Length is Distance along Circumference so its value depends on radius

Arc & Central Angle

• When a circles center is the vertex of an angle, it divides a circle into two arcs

• The Minor Arc is Acute and uses 2 Points to name ex: AB

• The Major Arc is a Reflex angle and uses 3 points to name  ex: ADB

Major & Minor Arc

When a circles center is the vertex of an angle, The Central Angle divides a circle into two arcs

The Minor Arc is Acute and uses 2 Points to name ex: AB

The Major Arc is a Reflex angle and uses 3 points to name ex: ADB

Multiple Choice

This is a picture of ___________. Hint: big or Small

• Minor Arc

• Major Arc

• Semi-Circle

Multiple Choice

Which is true of a minor arc?

• It forms half a circle.

• It forms a whole circle.

• It measures less than 180 degrees.

Multiple Choice

Name a minor arc. Hint Small Arc

• AD

• ADB

• AB

Multiple Choice

This is a picture of ___________. Hint: big or Small

• Minor Arc

• Major Arc

• Semi-Circle

Multiple Choice

Name a semicircle.

• AD

• ABC

• BA

Multiple Choice

If the measure of arc ABC = 210°, what is the measure of ∠AOC? Hint: Angle AOC is equal to 360 - Angle ABC

• 150°

• 100°

• 210°

Multiple Choice

Find the measure of arc JH

• 93
• 130
• 120
• 95

Multiple Select

Choose all of the correct answers.

• BAC is a minor arc and its measure is 290 degrees

• ABC is a semicircle and its measure is 180 degrees

• EBD is a major arc and its measure is 315 degrees

• DC is a minor arc and its measure is 70 degrees

Multiple Select

Choose all of the correct answers.

• EAB is a major arc and its measure is 180 degrees

• EAB is a semicircle and its measure is 180 degrees

• ABC is a is a semicircle and its measure is 180 degrees

• DC is a minor arc and its measure is 65

Multiple Choice

Solve for the missing angle. Hint: Angle C is a Central Angle congruent a minor angle.

• 45^o

• 90^o

• 22.5^o

Multiple Choice

Solve for x. Hint: Angle 85 is a Central Angle and is congruent to a minor angle. Solve

• 5

• 20

• 40

Radians

A radian is defined as the angle formed when a central angle has the same radius as the subtended arc.

So if S is arc length, then S=r

1 radian is about  $57^o$  

Pi & Radians

• Since  $360^o=2\pi\left(radians\right)$  

• A whole circle has 2pi or about 6.3 radians of arc

• A Semicircle has Pi radians of arc

Radian Conversion

You can use thei proportion to solve for either degrees(D) or radians(R). plug in your know value (R or D) and solve for the other

Converting Hints

• If you convert from Degrees, pi will show up in your answer for radians....

• Leave Pi as a symbol in radians! (unless you need a decimal answer)

• If you converting from Radians, pi will cancel out

Multiple Choice

 $180\degree=\pi$ rad

• TRUE

• FALSE

Multiple Choice

Convert 35π / 18 radians into degrees

• 350^o

• 340^o

• 355^o

• 345⁰

Multiple Choice

Convert 210^o to Radians

• 7π / 6

• 21π / 10

• 5π / 6

• 9π / 4

Multiple Select

Which are true about radians?

• 1 Radian is the angle where arc and radius are equal

• There are 2pi radians in a circle

• 1 radian is about 57 degrees

• A circumference is about 6.3 radians of arc

Multiple Select

Which of the following are true?

• $2\pi\left(radians\right)=360^o$

• $\pi\left(radians\right)=180^o$

• $\frac{\pi}{2}\left(radians\right)=90^o$

• $\frac{\pi}{3}\left(radians\right)=60^o$

Multiple Select

Which of the following are true?

• $\frac{\pi}{6}\left(radians\right)=60^o$

• $\frac{\pi}{10}\left(radians\right)=18^o$

• $\frac{\pi}{4}\left(radians\right)=45^o$

• $1\left(radian\right)=\left(\frac{180}{\pi}\ \right)^o$

Arc Length

You need the arc(in radians) and radius to find the Arc Length.

If you have degrees for angle measure, you can convert first or use this equation that has conversion in it...

Multiple Choice

Find the arc length indicated by the bolded arc. 

• 8.4 mi
• 9.4 mi
• 60.2 mi
• 117.8 mi

You finished!

now you can relax

Multiple Choice

Find the arc length indicated by the bolded arc. 

• 17.3 km
• 79.1 km
• 95.0 km
• 99.0 km

Multiple Choice

Find the length of the arc to 2dp

• 43.98cm

• 439.82cm

• 219.91cm

• 21.99cm

Multiple Choice

Find the length of the arc to 2dp

• 31.42cm

• 15.71cm

• 282.74cm

• 23.56cm

Tangent Lines & Tangent Ratios...are they the same?

If youre interested int this question, open tis link

https://bit.ly/3h3IOJ3

..otherwise you're finished!