Lesson 4 Circles Inside Out Solidify Understanding

Ready

Draw the altitude from vertex $A$ in each of the triangles. Then use trigonometry to find the height of the altitude. Leave your answer in terms of $\sin θ$ , $\cos θ$ , or $\tan θ$ .

(Hint: Answer will look something like this: $H = n \sin θ$ )

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Line $S T$ is tangent to radius $R S$ . (Figure 1)

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What is the measure of $∠ R S T$ ?

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Suppose you could drag point $S$ to a different position on the circle. Does the measure of $∠ R S T$ change? Explain.

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Segment $S T$ is tangent to circle $R$ in Figure 2. The measure of $∠ S R T = 53$ . Find $m ∠ R T S$ .

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Segments $A B$ and $C B$ are tangent to circle $P$ . Find the measure of $∠ A B C$ . (Figure 3)

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Draw line segment $P B$ on Figure 3. Find the radius of circle $P$ , given that $P B = 32 in.$

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Use Figure 4 to prove that $△ W X Y ≅ △ W Z Y$ . (Segments $X Y$ and $Z Y$ are tangent to circle $W$ .)

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Use Figure 5 to find $m ∠ L M N$ and $m ∠ L K N$ .

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The sides of $△ A B C$ (Figure 6) are tangent to $⨀ P$ at $D$ , $E$ , and $F$ .

$A B = 9$

$B C = 12$

$A C = 15$

What kind of triangle is $△ A B C$ ? Justify your answer.

Draw $\overset{―}{P D}$ and $\overset{―}{P F}$ . What can you conclude about quadrilateral $D P F B$ ? Justify your answer.

Label $\overset{―}{P D}$ and $\overset{―}{P F}$ with length $r$ .
Write the lengths of $\overset{―}{C E}$ and $\overset{―}{C F}$ in terms of $r$ .
Write the lengths of $\overset{―}{A D}$ and $\overset{―}{A E}$ in terms of $r$ .

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Construct a line tangent to circle $A$ and through point $T$ .

Go

Write the trigonometric equation needed to solve for angle $x$ . Then solve for $x$ .

Lesson 4 Circles Inside Out Solidify Understanding

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