LESSON 11.4 PART II SEGMENT LENGTHS

1
LESSON 11.4 PART II SEGMENT LENGTHS
OBJECTIVE To find lengths of segments
associated with circles
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Theorem 11-12 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
THE CIRCLE
There are three cases
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Case I. Intersection Point (P) Inside
a
c
b
P
FORMULA
d
ab cd
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Case II. Intersection Point (P) Outside
P
w
y
x
z
FORMULA
(w x)w (y z)y
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Case III. Intersection Point (P) Outside One
Segment Tangent
FORMULA
(y z)y t2
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EXAMPLES
1.
8cm
6cm
7cm
y
(6 8)6 (7 y)7
84 49 7y
35 7y
5cm y
7
z
2.
16in.
8in.
Round to the nearest tenth
z2 (16 8)8
z2 (24)8
z2 192
13.9 in. z
8
PRACTICE
20ft
3.
14ft
x
16ft
x
(20 14)14 (x 16)16
(34)14 16x 256
476 16x 256
220 16x
13.8ft. x
9
3in
4.
m
6.5in
7in
3(7) 6.5m
21 6.5m
3.2in. m
10
5.
x
8cm
2.5
2
2x 8(2.5)
2x 20
x 10 cm
11
6.
y2 (2 9)2
9
y2 (11)2
2
y2 22
y 4.7
y
ASSIGNMENT Page 611 9-14, 20-25, 39, 40