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CIRCLE RELATIONSHIPS
Can you draw a radius to each point of tangency?
What do you notice about the radius in each picture?
Picture 1 Picture 2 Picture 3
Where is vertex?Name of Angle
Formula:
Identify the type of angle. Then, find the missing value.
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How can we measure the length of a football field?
Just as we can measure a football field in yards or feet, we can measure a circle in more than one way!
Introducing… Radians!• You’re used to thinking of a circle in terms of
degrees: 360° is the whole circle. 180° is half the circle, etc...
• Radian measure is just a different way of talking about a circle.
Think about what the word radian sounds like…
It turns out that a radian has a relationship to the radius of a circle!
That’s why the circumference of a circle can be found using the formula:
rC 2
You’ve seen radians without even knowing it!
Converting
Remember: Where you are going is more important than where you are coming from!
Given radians:
Given degrees:
180
bymultiply
180
bymultiply
Arc Length
An arc of a circle is a portion of the circumference formed by a central angle.
It’s the length of the pie crust!
θ
Arc Length
The arc length s of a circle radius r, subtended by a central angle of θ radians, is given by:
s = rθ The angle must ALWAYS BE IN
RADIANS. Sometimes it will be given in
degrees to trick you. Convert it to radians!
Find the length of the arc of a circle of radius 4 meters subtended by a central angle of 0.5 radian.
Example 1: Arc Length
“Subtended?” That just means
“formed by.”
Area of a Sector
A sector of a circle is a portion of the circle formed by a central angle.
It’s the area of a slice of pie!
θ
Area of a Sector
The area of a sector A of a circle radius r, subtended by a central angle of θ radians, is given by:
A = ½r2θAgain, the angle must
ALWAYS BE IN RADIANS. Sometimes
it will be given in degrees to trick you. Convert it to radians!
Find the area of the sector of a circle of radius 5 feet subtended by an angle of 60°. Round the answer to two decimal places.
Example 2: Area of a Sector
“Subtended?” That just means
“formed by.”
Put it all together!Arc Length Area of a Sectors = rθ A = ½r2θLength of pie crust Area of a slice
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