1. Tangents Solve problems involving circumscribed polygons.
Use properties of tangents.
Solve problems involving circumscribed polygons.

2. TANGENTS I
radius A C B
tangent to circle
point of tangency
AC is tangent to circle I because the line containing AC intersects the circle at exactly one point. This point is called the point of tangency.

3. Theorem
If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. I
radius A C B
tangent to circle
point of tangency

4. Example 1 Find Lengths ED is tangent to circle F at point E. Find x. 43 x

5. Theorem
If a line is perpendicular to the radius of a circle at its endpoint on the circle, then it is tangent to the circle. I
radius A C B
tangent to circle
point of tangency

6. Example 2 Identify Tangents
Determine whether MN is tangent to circle L. L 3 O 2 M 4 N

7. Example 3 Identify Tangents
Determine whether PQ is tangent to circle R. 4 R P S 5 4 Q

8. MORE THAN ONE TANGENT
More than one line can be tangent to the same circle. A D B C

9. Theorem
If two segments from the same exterior point are tangent to a circle, then they are congruent. A B C

10. Example 4 Solve a Problem Involving Tangents
Find x A
6x + 5 C
-2x + 37 Q R B

11. Example 5 Triangles Circumscribed About a Circle
Find the perimeter of triangle ADC if EC = DE + AF. D 6 E F C A B 19