Download Geometry Lesson 11-3 Inscribed Angles.notebook

Geometry Lesson 11­3 Inscribed Angles.notebook
April 16, 2013
Section 11­3 : Inscribed Angles
Warm ­ Up
T
Identify the following in Circle P.
1. a semicircle
86o
2. a minor arc
P
Q
145o
S
3. a major arc
R
4. a central angle
The vertex of <C is on circle O, and the sides of <C are chords of the circle, <C is an inscribed angle. AB is the intercepted arc of <C.
A
B
C
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Geometry Lesson 11­3 Inscribed Angles.notebook
April 16, 2013
Theorem 11­9 : Inscribed Angle Theorem ­ The measure of an inscribed angle is half the measure of its intercepted arc. 1
m<B = m AC
2
B
A
C
Example 1) Find the values of a and b.
You try) Find m<PQR if m RS = 60.
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Geometry Lesson 11­3 Inscribed Angles.notebook
April 16, 2013
Corollaries to the Inscribed Angle Theorem: (1) Two inscribed angles that intercept the same arc are congruent. (2) An angle inscribed in a semicircle is a right angle. (3) The opposite angles of a quadrilateral inscribed in a circle are supplementary. Example 2) Find the measure of the numbered angles.
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Geometry Lesson 11­3 Inscribed Angles.notebook
April 16, 2013
Theorem 11­10: The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc.
1
m<C = mBDC
2
Example 3) In the diagram at the right, KJ is tangent to the circle at J. Find the values of x and y.
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