Warm Up
Identify the parts of thecircle
10 minutes
End
Circle Relationships
Unit 6 Day 2
Angle Properties
-Angle formed by a Tangent and Radius
-Central Angle of a Circle
-Angles formed by 3 points on a circle (Inscribed)
-Angles formed by secants or tangents
Can you draw a radius to each point of tangency?
What do you notice about the angle formed by the radius andtangent line in each picture?
Radius and Tangent
A radius and a tangent line meet at a 90º angle.
Picture 1
Picture 2
Picture 3
Where isvertex?
Name of Angle
Formula:
Center
Central Angle
On the circle
Inscribed Angle
Outside the circle
***
Finding Length and Area
Angles can be measured by DEGREES orRADIANS
*Think centimeters and inches
A full trip around a Circle is 360 degreesOR 2π radians
Converting between Degrees andRadians
To Convert from degree to radian
PART(degree)
Whole (360)
To Convert from radians to degree
PART(radian)
Whole (2π)
X 2π
X 360
Examples
Convert the following.
1.150 degrees
2.45 degrees
1.3π/2
1.π/6
Arc Length Formulas
We have two formulas to find arc length. Decided which to use baseoff of the information we are given:
Degrees:
Radians:
Area of a Sector
Again, we have two different formulas to find the area of a sector.
Degrees:
Radians:
