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Unit 9, Lesson 8
Tangents, part 2
"Inspiration is needed in geometry, just as much as in poetry."
- Aleksandr Pushkin
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Example 1:
Hint: What type of angle is BAC?
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Example 2:
Hint: Can you make this look
like the last problem?
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Example 3:
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Examples 1-3 were dealing with a certain type of angle...
How was this angle formed?
How does this angle measure compare with its intercepted arc?
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Computer Activity
1. Go to my website (www.tinyurl.com/WrightGeometry)
2. Scroll down to Unit 9, Lesson 8 and select the Tangent and Chord Link.
3. Answer the following questions
Use the gray dots to change the location tangent and chord. Try several different arrangements.
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Q1: Does this activity support your idea from the first 3 questions?
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Theorem 9-8
The measure of an angle formed by a chord and a
tangent is equal to half the measure of the intercepted arc
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Common Tangents
External Common Tangents
-Does not intersect segment
connecting centers
Internal Common Tangents
-Intersects segment
connecting centers
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Tangent Circles
-coplanar circles tangent to the same line at the same point
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Example 4:
Circle P and S are internally tangent at Q, and PR is tangent to circle S at T.
The radii are 8 and 3, find QR.
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Example 5:
In the figure each of the circles with centers A, B, and C are tangent to
the other two. If AB = 10, AC = 18, and BC = 22, find the radius of
each circle.
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Example 6:
The distance between the centers of two circles, having radii of 4 and 10, is 21.
How long is the common internal tangent segment?
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Example 7
Is it possible for two circles to have no common tangents?
1 common tangent?
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