Tangents to

1
Chapter 7 The Circle
7.5
Tangents to a Circle
7.5.1
MATHPOWERTM 11, WESTERN EDITION
2
Tangent to a Circle
A tangent to a circle is a line that intersects
the circle at exactly one point. The point where
the tangent intersects the circle is called the
point of tangency.
Tangent
Point of Tangency
7.5.2
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Tangent Theorems

• A tangent to a circle is perpendicular to the
• radius at the point of tangency.
• The tangent segments to a circle from any
• external point are congruent.

7.5.3
4
Tangent Theorems contd

• The angle between a tangent and a chord is
• equal to the inscribed angle on the opposite
• side of the chord.

These two angles are equal.
800
400
400
7.5.4
5
Using the Tangent Theorems
3
500
1
2
650
1. ______ 2. ______ 3. ______
650
650
7.5.5
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Using the Tangent Theorems
The sum of the angles of a quadrilateral is 3600.
900
650
X
500
650
250
900
900
1300
X _______
7.5.6
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Using the Tangent Theorems
700
1. ______ 2. ______ 3. ______ 4.
______ 5. ______
5
700
550
4
550
3
700
2
1
400
7.5.7
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Using the Tangent Theorems
Find the perimeter.
10 cm
15 cm
18 cm
c2 a2 b2 182 102 b2 b2 224 b 15
Therefore, the perimeter is 50 cm.
7.5.8
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Assignment
Suggested Questions
Pages 431 and 432 1-14, 16, 18, 19, 20
7.5.9