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

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Warm Up Identify the parts of the circle 10 minutes End

Unit 6 Day 2 Circle Relationships

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 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.

On the circle Center Central Angle Inscribed Angle Outside the circle Picture 1 Picture 2 Picture 3 Where is vertex? Name of Angle Formula: Center On the circle Outside the circle Central Angle Inscribed Angle ***

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 2π 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 (2π) X 2π X 360

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