# Lesson 4Circles Inside OutSolidify Understanding

## Ready

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 .

• What kind of triangle is ? Justify your answer.

• Draw and . What can you conclude about quadrilateral ? Justify your answer.

• 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 .