1. 6.5 Apply Other Angle Relationships in Circles
Pg. 212

2. Todays Goals
Use angles formed by tangents and chords to solve problems in geometry
Use angles formed by lines that intersect a circle (i.e. _________) to solve problems
Basically, we are going to examine angle and arc measures when chords, secants and/or tangents intersect ____, ________, ________ a circle

3. Where is the ________ ?? ___ the Circle _____________ (2 ________ )
_____________ (2 ________ )
(1 __________, 1 __________)
Angle Arc
Angle Arc
Also notice how the tangent and the chord form supplementary angles

4. Rule for Vertex on the Circle: ______ = ______ intercepted arc
Ex. Line m is tangent to the circle. Find the indicated measure.
___________ b _____________
In the diagram below, Line BC is tangent to the circle. Find
Practice: Textbook p212 GP #1 – 3 1) _________ 2) __________ 3) _________ 1

5. __________ the Circle And ____ the ________ Angle Arc Angle Arc
Also notice how the 2 chords form vertical and supplementary angles
Rule for Vertex IN the Circle: angle = (_____ of ________ intercepted arcs)

6. CAUTION ABOUT VERTICAL ANGLES !!!!!
If the vertex of the angle is INSIDE the circle (ON or OFF the center), the angle is always half the sum of the measures of the arcs intercepted by the angle and its vertical angle.
CAUTION ABOUT VERTICAL ANGLES !!!!!
VS.
not the same!

7. Find “x”
Textbook p ex. 2, 3, and GP #4

8. Rule for Vertex OUTSIDE the Circle: ____ = (_____ ARC - _____ ARC)
Can we use chords to form an angle OUTSIDE THE CIRCLE ?
_________
Angle Arc
Angle Arc
Angle Arc
Rule for Vertex OUTSIDE the Circle: ____ = (_____ ARC - _____ ARC)

9. Find the value of “x”

10. Summary of Angle-Arc Relationships
Depending on location of the Angle’s Vertex
Vertex
Angle/Arc Relationship
Central
(on Center) =
Inscribed
Inside and (off Center)
Outside

11. Homework
Pg. 214 – – 19 all