12.4 Angle Measurements and Segment Lengths

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

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

Secants

• A secant is a line that intersects a circle at two points.

Finding Angle Measures

• What is the value of each variable?

1(46 90)2

x

68x

120 (95 )

2z

40 95 z 55z

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.

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

More Practice!!!!!

• Homework – Textbook p. 794 #8 – 13, p. 795 #15 – 20 ALL.