Basic Angles and Arcs of Circles

Circles Unit Test Review

​Parts of a circle

Center: You name a circle by its center.

Radius: A segment from a point on the circle to the circle’s center

Chord: A segment whose endpoints lie on the circle
Diameter: A chord that goes through the center of the circle

Secant: A line that intersects a circle at two points

Tangent: A line or segment that intersects a circle at exactly one point

3 Types of Arcs: semicircles, minor arcs, and major arcs.

A semicircle is an arc of a circle whose endpoints are the endpoints of a diameter. The measure of a semicircle is 180°.

A minor arc is an arc of a circle that is less than a semicircle of the circle. The measure of a minor arc is less than 180°.

A major arc is an arc of a circle that is greater than a semicircle of the circle. The measure of a major arc is greater than 180°.

Multiple Choice

Describe the following part of the circle:

BE

• Chord

• Radius

• Center

• Diameter

Multiple Choice

Describe the following part of the circle:

AD

• Diameter

• Chord

• Secant

• Tangent

Multiple Choice

Describe the following part of the circle:

B

• Tangent

• Chord

• Center

• Radius

Multiple Choice

Describe the following part of the circle:

CE

• Diameter

• Secant

• Chord

• Tangent

Multiple Choice

Describe the following part of the circle:

FC

• Radius

• Tangent

• Chord

• Secant

Multiple Choice

Which of the following is a major arc?

• AFC

• ACE

• AF

• CE

Multiple Select

Which of the following are minor arcs?

• AFC

• ACE

• AF

• CE

Multiple Choice

Which of the following is a semicircle?

• AFC

• ACE

• AF

• CE

Draw

Draw a picture of your favorite animal

Equation of a circle

(x-h)²+(y-k)²=r²

• What does (h,k) represent?

• What does r represent?

Two things to remember when finding an equation of a circle

You square your radius before putting it in the equation

​Square r

(h,k) becomes -h and -k in your equation.

Flip the signs

Multiple Choice

What is the center and radius of the following circle?

(x + 3)² +  ( y - 1)²  =  25

• (3, -1)

  r=5

• (-3, 1)

  r=25

• (-3, 1)

  r=5

• (3, -1)

  r=25

Multiple Choice

What is the equation of a circle with center (4, -8) and radius 9?

• (x-4)²+(y+8)²=81

• (x-4)²+(y-8)²=81

• (x+4)²+(y+8)²=81

• (x-4)²+(y+8)²=9

Poll

What's your favorite candy?

• Anything Chocolate

• Sour Patch

• Sour Gummy Worms

• Nerd Gummy Clusters

​Arc Length and Sector Area

Arc Length= n/360(2πr)
Sector Area= n/360(πr²)

Arc length is a fractional part of the circumference of a circle
Sector area is a fractional portion of the circle's area

Multiple Choice

Find the arc length.

• 130 m

• 3.4 m

• 40.8 m

• 13.6 m

Multiple Choice

Find the sector area.

• 127 m²

• 75.4 m²

• 135 m²

• 18.8 m²

Word Cloud

What is your favorite color

Converting radians and degrees

n × 180/π=degrees

radians to degrees

n^o × π/180=radians

degrees to radians

Remember:

• Don't plug the π into the calculator, just put your leftover π next to your answer

• Put calculator into fraction mode

Draw

Convert the following angle measure from degrees to radians.

300^o

Draw

Convert the following angle measure from radians to degrees.

2π/3

Fill in the Blank

Why are circles so smart?

Central and Inscribed Angles

Central Angle: Angle at the center of the circle



Inscribed Angle: Angle formed by two chords with a common endpoint

• The measure of an inscribed angle is half the measure of the intercepted arc

Inscribed Angles

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

​Central Angles

Multiple Choice

What is the measure of x?

• 60.5^o

• 242^o

• 239^o

• 121^o

Multiple Choice

What is the measure of y?

• 60.5^o

• 242^o

• 239^o

• 121^o

Multiple Choice

What is the measure of x?

• 103^o

• 51.5^o

• 206^o

• 257^o

Multiple Choice

What is the measure of arc FE?

• 17.5^o

• 70^o

• 145^o

• 35^o

Poll

What's your most used social media?

• Tik Tok

• Instagram

• Twitter (X?)

• Snapchat

• Other

​Circle Angles

• The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc

​71^o

​Circle Angles

• Inscribed angles that intercept a semi circle are right angles

​Circle Angles

• Opposite angles in a cyclic quadrilateral are supplementary (add to 180^o)

Multiple Choice

What is the measure of angle C?

• 90^o

• 100^o

• 360^o

• 180^o

Multiple Choice

What is the measure of angle C?

• 105^o

• 187^o

• 173^o

• 68^o

Fill in the Blank

Why was the obtuse angle always sad?

Angles Formed by Chords, Secants, & Tangents

Inside Angles

• When two chords intersect inside the circle, the measure of each angle formed is half the sum of the measures of the arcs intercepted by the angle and its vertical angle

• Formula:

  • (a+b)/2

Angles Formed by Chords, Secants, & Tangents

Outside Angles

• The measure of an angle formed by secants and/or tangents that intersect outside the circle is half the difference of the measure of the intercepted arc

• Formula:

  • (a-b)/2

  • (big-small)/2

Multiple Choice

What is the measure of x?

• 111^o

• 13^o

• 75^o

• 173^o

Multiple Choice

What is the measure of x?

• 104^o

• 82^o

• 42^o

• 102^o

Multiple Choice

What is the measure of x?

• 115^o

• 65^o

• 180^o

• 187.5^o

Open Ended

A + B + C = D, and A x B x C = D. What numbers make these two equations true?