10-6 Find Segment Lengths in Circles

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10-6 Find Segment Lengths in Circles
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Segments of Chords Theorem
If two chords intersect in the interior of a
circle, then the product of the lengths of the
segments of one chord is equal to the product of
the lengths of the segments of the other chord.
q
m
n
m n p q
p
3
example solve for x
8 3 6 x
3
x
24 6x
6
4 x
8
4
Definitions
R

• Tangent Segment a piece of a tangent with one
  endpoint at the point of tangency.
• Secant Segment a piece of a secant containing a
  chord, with one endpoint in the exterior of the
  circle and the other on the circle.
• External Secant Segment the piece of a secant
  segment that is outside the circle.

S
SP
Q
RP
P
PQ
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Segments of Secants Theorem
If two secant segments share the same endpoint
outside a circle, then the product of the lengths
of one secant segment and its external segment
equals the product of the lengths of the other
secant segment and its external segment.
C
AB AC AD AE
E
B
D
A
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example solve for x

• 11 21 12 (12 x)
• 231 144 12x
• 87 12x
• 7.25 x

10 11 21
10 11
x 12
X 12
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Segments of Secants and Tangents Theorem
If two secant segments share the same endpoint
outside a circle, then the product of the lengths
of one secant segment and its external segment
equals the product of the lengths of the other
secant segment and its external segment.
B
A
(AB)2 AC AD
C
D
8
example solve for x

• 302 x (x 24)
• 900 x2 24x
• x2 24x 900 0
• How do you solve for x?
• Use the quadratic formula!!
• x 20.31 x -44.31

24
30
a 1 b 24 c -900
x
9
example solve for x
220
1st Find the other arc
360 140 220
140
220 140 x 2
x
80 x 2
40 x