12.4 angle measurements and segment lengths
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12.4 Angle Measurements and Segment Lengths. Theorem 12.13 The measure of an angle formed by two lines that intersect inside a circle is half the sum of the measures of the intercepted arcs. Theorem 12.14. Theorem 12.14 - PowerPoint PPT PresentationTRANSCRIPT
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12.4 Angle Measurements and Segment Lengths
• Theorem 12.13– The measure of an angle formed by two lines that intersect
inside a circle is half the sum of the measures of the intercepted arcs.
11 ( )2
m x y
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Theorem 12.14
• Theorem 12.14– The measure of an angle formed by two lines that intersect
outside a circle is half the difference of the measures of the intercepted arcs.
11 ( )2
m x y
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Secants
• A secant is a line that intersects a circle at two points.
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Finding Angle Measures
• What is the value of each variable?
1(46 90)2
x
68x
120 (95 )
2z
40 95 z 55z
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Theorem 12.15
• Theorem 12.15– For a given point and circle, the product of the lengths of the
two segments from the point to the circle is constant along any line through the point and circle.
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Finding Segment Lengths
• Find the value of the variable in circle N.
(6 8)6 (7 )7y
84 49 7y 35 7y
5y
2(8 16)8 z 2192 z2192 z
13.9z
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More Practice!!!!!
• Homework – Textbook p. 794 #8 – 13, p. 795 #15 – 20 ALL.