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Section 9.5

Section 9.5. INSCRIBED ANGLES. Inscribed Angle. What does inscribe mean? An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An inscribed angle is equal to half of

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Section 9.5

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  1. Section 9.5 INSCRIBED ANGLES

  2. Inscribed Angle • What does inscribe mean? • An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An inscribed angle is equal to half of its intercepted arc chord 1 chord

  3. 1 2 Central vs. Inscribed • How are central angles related to the arcs they make? Central Angles are = to the arcs radius radius chord Inscribed Angles are = ½ of the arcs chord

  4. o o o o 1) Find the values of x and y. x is opposite of the inscribed angle of 20o x = 40o y = 75o y is the inscribed angle of the arc including 110o and 40o x = 40o y = ½(150o) = 75o

  5. o o o o 2) Find the values of x, y, and z. y is a central angle of arc of 60o y = 60o y = 60o x is an inscribed angle of arc of 60o zo x = ½(60o) = 30o x = 30o 360 – 60 = 300 = 2z z = 150o

  6. Semicircles • Draw a circle. • Draw a diameter and label the points A & B. • Label another point Q on the circle. • Highlight the semicircle around these letters. • Draw ∠AQB. • What should be true about that angle ALWAYS? Q An angle inscribed in a semicircle is a right angle. A B

  7. o o o Center 3) Find the values of x and y.A diameter is pictured. y = 90o because it is an inscribed angle of a semicircle 40o x = 20o because it is an inscribed angle of this arc

  8. Quads and Circles • Draw a circle. • Inscribe a quadrilateral into a circle. • Label the points of the quadrilateral DOGS. • What do you think is true about the opposite angles? If a quad. is inscribed into a circle, then its opp. angles are supplementary. D O S G

  9. Last one! • The measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc. m∠1 = ½(140o) = 70o What is the m∠1? 140 chord 1 tangent

  10. o o o o 4) Find the values of x, y, and z. x is opposite of 82o so they are supplementary. 164o 98o x = 98o y and z are congruent angles because their chords are congruent. 98o y and z are inscribed so 98/2 = 49o 360 – 164 = 196 196/2 = 98o

  11. Practice Problems • Page 353 • Classroom Exercises • #4 - 9 • DRAW ALL DIAGRAMS

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