Warm Up Identify the parts of the circle 10 minutes End.

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Presentation transcript:

Warm Up Identify the parts of the circle 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 and tangent line in each picture?

Radius and Tangent A radius and a tangent line meet at a 90º angle.

Picture 1Picture 2Picture 3 Where is vertex? 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 or RADIANS *Think centimeters and inches A full trip around a Circle is 360 degrees OR 2 π radians

Converting between Degrees and Radians To Convert from degree to radian PART(degree) Whole (360) To Convert from radians to degree PART(radian) Whole (2 π ) X 2 π X 360

Examples Convert the following degrees degrees 1. 3 π /2 1. π /6

Arc Length Formulas We have two formulas to find arc length. Decided which to use base off 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: