### Segments from Secants and Tangents

If a tangent and secant meet at a common point outside a circle, the segments created have a similar relationship to that of two secant rays.

**Tangent Secant Segment Theorem:** If a tangent and a secant are drawn from a common point outside the circle (and the segments are labeled like the picture below), then .

What if you were given a circle with a tangent and a secant that intersect outside the circle? How could you use the length of some of the segments formed by their intersection to determine the lengths of the unknown segments?

### Examples

#### Example 1

Find . Simplify any radicals.

Use the Tangent Secant Segment Theorem.

#### Example 2

Find . Simplify any radicals.

Use the Tangent Secant Segment Theorem.

#### Example 3

Find the length of the missing segment.

Use the Tangent Secant Segment Theorem.

#### Example 4

Fill in the blank and then solve for the missing segment.

#### Example 5

Find the value of the missing segment.

Use the Tangent Secant Segment Theorem.

### Review

Fill in the blanks for each problem below and then solve for the missing segment.

Find in each diagram below. Simplify any radicals.

- Describe and correct the error in finding .

Solve for the unknown variable.

### Review (Answers)

To see the Review answers, open this PDF file and look for section 9.11.