# Lesson 4Circles Inside OutSolidify Understanding

Draw the altitude from vertex in each of the triangles. Then use trigonometry to find the height of the altitude. Leave your answer in terms of , , or .

(Hint: Answer will look something like this: )

## Set

Line is tangent to radius . (Figure 1)

### 5.

What is the measure of ?

### 6.

Suppose you could drag point to a different position on the circle. Does the measure of change? Explain.

### 7.

Segment is tangent to circle in Figure 2. The measure of . Find .

### 8.

Segments and are tangent to circle . Find the measure of . (Figure 3)

### 9.

Draw line segment on Figure 3. Find the radius of circle , given that

### 10.

Use Figure 4 to prove that . (Segments and are tangent to circle .)

### 11.

Use Figure 5 to find and .

### 12.

The sides of (Figure 6) are tangent to at , , and .

• Label and with length .

• Write the lengths of and in terms of .

• Write the lengths of and in terms of .

### 13.

Construct a line tangent to circle and through point .

## Go

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