Chapter 12 key words: Chapter 12 key words
Angle and Arc Measures: Angle and Arc Measures
Slide 3: Central Angle: an angle whose vertex is at the center of the circle and its sides are radii of the circle. 45 x What is the value of x? 45 In a central angle the angle measure is _________ the intercepted arc. EQUAL TO
Slide 4: x 30 Inscribed Angle: an angle whose vertex is on the circle and its sides are chords of the circle. What is the value of x? 60 In an inscribed angle the angle measure is _________ the intercepted arc. HALF OF
Slide 5: An angle created by a chord and a tangent has its vertex on the circle. The angle measure is _________ the intercepted arc measure. HALF OF X What is the value of x? 100 50
Slide 6: To find the measure of an angle inside the circle that does not have the vertex in the center or on the circle, you ______________________________ ADD THE ARCS AND DIVIDE BY 2 X What is the value of x? 40 50 50 + 40 2 = X 90 2 = X 45 = X
Slide 7: To find the measure of an angle outside the circle, you __________________________________ SUBTRACT THE ARCS AND DIVIDE BY 2 What is the value of x? 100 - 30 2 = X 7 0 2 = X 3 5 = X X 3 0 100
Finding missing segment lengths in chords, tangents, and secants: Finding missing segment lengths in chords, tangents, and secants
Slide 9: If you have 2 chords, the product of the segments of the 1 st chord equals the product of the segment of the 2 nd chord Two Chords a b d c a b = cd = 6 = 9 = 6 = 4 4(9) = 6(6) 36 = 36
Slide 10: If you have 2 secants, the product of the entire length of the 1 st secant and the external portion of the secant equals the product of the entire length of the 2 nd secant and the external portion of the secant Two Secants a b = c d 20( 2 ) = 10( 4 ) 40 = 40 a d b c = 20 = 10 = 2 = 4
Slide 11: If you have 2 secants, the product of the entire length of the 1 st secant and the external portion of the secant equals the tangent segment squared Secant and Tangent a b = c 2 9 (4) = 6 2 36 = 36 a b c = 9 = 4 = 6