1. Unit 6 Day 2
Circle Relationships

2. https://play. kahoot. it/#/lobby
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3. Angle Properties Tangent and Radius Angle Central Angle of a Circle
Angles formed by 3 points on a circle (Inscribed)
Angles formed by secants or tangents (Circumscribed)

4. Can you draw a radius to each point of tangency
Can you draw a radius to each point of tangency? What do you notice about the radius in each picture?

5. Radius and Tangent
Radius and Tangent meet at 90 degree angles.

6. Picture 1
Picture 2
Picture 3
Where is vertex?
Name of Angle
Formula:

10. Degrees vs. Radians
Objects can be measured in many ways, think centimeters or inches. Angles are the same way. Angles can be measured by DEGREES or RADIANS A full trip around a Circle is 360 degrees OR 2π

11. Converting between Degrees and Radians
To Convert from degree to radian To Convert from radians to degree

12. Examples
Convert the following.
150 degrees
45 degrees
3π/2
π/6

13. 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

14. 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!

15. 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

16. 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 = ½r2θ
Again, the angle must ALWAYS BE IN RADIANS. Sometimes it will be given in degrees to trick you. Convert it to radians!