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 its intercepted arc 1 chord

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

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

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

1)Draw a circle. 2)Draw a diameter and label the points A & B. 3)Label another point Q on the circle. 4)Highlight the semicircle around these letters. 5)Draw ∠ AQB. 6)What should be true about that angle ALWAYS? Q Semicircles A B An angle inscribed in a semicircle is a right angle.

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

Quads and Circles 1)Draw a circle. 2)Inscribe a quadrilateral into a circle. 3)Label the points of the quadrilateral DOGS. 4)What do you think is true about the opposite angles? If a quad. is inscribed into a circle, then its opp. angles are supplementary. DO GS

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

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

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