11-1 Tangent Lines

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11-1Tangent Lines
Objective To use the relationship between two
tangents from one point.
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Vocabulary

• Inscribed in
• Circumscribed about

• All vertices of a figure lie on the circle.
• When a circle is inscribed in a figure.

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1 Finding a Tangent

• A belt fits tightly around two circular pulleys.
  Find the distance between the centers of the
  pulleys.

15 cm
3 cm
15 cm
3 cm
4 cm
O
P
x
7 cm
15 cm
4
2 Finding a Tangent
35 cm
A belt fits tightly around two circular pulleys,
as shown. Find the distance between the centers
of the pulleys.
14 cm
8 cm
35 cm
6 cm
O
P
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Theorem 11-3

• The two segments tangent to a circle from a point
  outside the circle are congruent.

A
B
O
C
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3 Circles Inscribed in Polygons

• Circle O is inscribed in Triangle PQR. Triangle
  PQR has a perimeter of 88 cm. Find QY.

Q
x
X
x
15 cm
P
Y
O
15 cm
Z
17 cm
17 cm
R
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4 Circles Inscribed in Polygons

• Circle O is inscribed in Triangle ABC. Find the
  Perimeter of Triangle ABC.

B
15cm
D
15cm
10 cm
A
E
O
10 cm
F
8 cm
8 cm
C
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Assignment

• Page 586
• 4-9 13-19