6.5 Apply Other Angle Relationships in Circles Pg. 212

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

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

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

__________ 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)

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!

Find “x” Textbook p. 213 ex. 2, 3, and GP #4

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)

Find the value of “x”

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

Homework Pg. 214 – 215 1 – 19 all