1. 10.6 Secants, Tangents, and Angle Measures
Then: You found measures of segments formed by tangents to a circle.
Now:
Find measures of angles formed by lines intersecting on or inside a circle.
Find measures of angles formed by line intersecting outside the circle.

2. Intersections On or Inside a Circle
Secant: a line that intersects a circle in exactly two points. Measures of the angles formed by secants and tangents are related to the intercepted arcs.

3. Theorem 10.12

4. Example 1: Use Intersecting Chords or Secants
Find each measure. Assume that segments that appear to be tangent are tangent. a. m1

5. Example 1:
c. m5

6. Theorem 10.13

7. Example 2: Use Intersecting Secants and Tangents

8. Example 2:
c. m6

9. Intersection Outside a Circle
When secants and tangents intersect outside a circle, they make angles whose measures are related to the intercepted arcs.

10. Theorem 10.14
If two secants, a secant and a tangent, or two tangents intersect in the exterior of a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs.
Two Secants:

11. Theorem 10.14
Secant-Tangent
Two Tangents

12. Example 3: Use Tangents and Secants that Intersect Outside a Circle
Find each measure. Assume that segments that appear to be tangent are tangent.
a. m1

13. Example 3:
b. m 2

14. Example 3:
c. m 3

15. Example 3:

16. Example 3:

17. Example 3:
f. mV

18. Example 4: Apply Properties of Intersecting Secants

19. 10.6 Assignment
p #8-16 all, all, 34, evens, 54, 56 SHOW ALL WORK!!!