1. Geometry Warm-Up4/5/11 1)Find x.2) Determine whether QR is a tangent.

2. 10-6: Secants, Tangents, & Angle Measures Geometry April 6, 2011

3. 3 places where lines can intersect: On the circle Inside the circle

4. 3 places where lines can intersect: Outside the circle

5. Theorem 10.12 If 2 chords intersect in the interior of a circle, then the measure of each angle is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

6. Theorem 10.14 If a tangent and a secant, two tangents, or two secants 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.

7. Example 1 Find the value of x.

8. Example 2 Find the value of x.

9. Example 3 Find x.