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Learn about the Inscribed Angle Theorem in Chapter 11 of Circles Geometry with examples. Understand how to find angle measures using intercepted arcs. Solve bellwork exercises on page 598 involving inscribed angles & angles intercepted by arcs. Discover corollaries related to inscribed angles in circles. Practice problems involving tangents, chords, and angles formed in a circle. Complete homework exercises on page 601, numbers 2 to 24 even. Get a grasp on key concepts and improve your geometry skills today!
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Bellwork Pg 598 1-8
11.3 Inscribed Angles Chapter 11 Circles
) <C is an inscribed angle. AB is the intercepted arc of <C. A Inscribed Angle Intercepted Arc C B
Theorem 11-9 Inscribed Angle Theorem: The measure of an inscribed angle is half the measure of its intercepted arc. m<B = ½ mAC ) A B C
a° ) m<PQT = ½ mPT P Find the values of a and b. 60 = ½ a T a = 120° 30° S ) m<PRT = ½ PS 60° b = ½ (a + 30) Q b = ½ (120 + 30) 60° b° b = ½ (150) b = 75 R ) Find m<PQR if mRS = 60 m<PQR = ½ ( a + 30 + 60) m<PQR = ½ (120 + 30 + 60) m<PQR = ½ (210) m<PQR = 105°
Corollaries to the Inscribed Angle Theorem: • Two inscribed angles that intercept the same arc are congruent. • An angle inscribed in a semicircle is a right angle. • The opposite angles of a quadrilateral inscribed in a circle are supplementary.
40° <1 is 90° because it is inscribed in a semicircle (180°) Find the measure of the numbered angle. 70° 1 <2 and the 38° intercept the same arc, so the angles are congruent. m<2 = 38° 70° 2 38°
Find the measure of each numbered angle. m<1 = 90° 1 m<3 = 90° m<4 = ½ (80 + 60) 80° 4 m<4 = 70° m<2 = 180 - 70 m<2 = 110° 2 3 60°
Theorem 11-10 The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc m<C = ½ mBDC ) B B D D C C
In the diagram, KJ is tangent to the circle at J. Find the values of x and y. ) x = ½ mJL ) ½ mJL = <Q ) J Q ½ mJL = 35° 35° x = 35° x° ) y° y = ½ QJ QJ = 180 - 70 L QJ = 110° y = ½ (110) K y = 55°
Homework: pg 601 2 – 24 even