Transcript Segment Formulas Lesson 8-6 Lesson 8-6: Segment Formulas

Lesson 8-6
Segment
Formulas
Lesson 8-6: Segment Formulas
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Intersecting Chords Theorem
Interior segments are formed by two intersecting chords.
Theorem:
If two chords intersect within a circle, then
the product of the lengths of the parts of
A
one chord is equal to the product of the
lengths of the parts of the second chord.
a
c
a•b=c•d
d
E b
B
C
Lesson 8-6: Segment Formulas
D
2
Intersecting Secants/Tangents
Exterior segments are formed by two secants, or a secant
and a tangent.
B
A
B
C
D
A
D
C
E
Two Secants
Secant and a Tangent
Lesson 8-6: Segment Formulas
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Intersecting Secants Theorem
If two secant segments are drawn to a circle from an
external point, then the products of the lengths of the
secant and their exterior parts are equal.
e
A
a
B
c
b
D
C
d
a•e=c•f
f
E
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Example:
In the figure; if BC  6cm, AD  2cm, AB  4cm . Find x .
A
B
C
AB  AC = AD  AE
4  10 = 2  (2+x)
D
40 = 4 + 2x
36 = 2x
E
X = 18 cm
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Secant and Tangent Theorem:
The square of the length of the tangent equals the product
of the length of the secant and its exterior segment.
B
a2 = b • d
a
b
c
A
D
C
d
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Example:
In the figure if AD  9 cm, and AC  25 cm. Find x.
AB  AD  AC
2
B
x  9  25
x
C
D
2
9 cm
A
x  225  15 cm
25 cm
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