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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 1 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. 2 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. 3 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. 4