This is the Luis I bridge in Portugal. There is an upper road and a lower road. The lower road intersected the circular

1. This is the Luis I bridge in Portugal. There is an upper road and a lower road. The lower road intersected the circular support arc in two places. This is called a secant of a circle.

2. 9.2 Tangents and Secants Tangents and secants are LINES. A tangent line intersects the circle at exactly ONE point. A secant line intersects the circle at exactly TWO points.

3. A little extra information The word tangent comes from the Latin word meaning to touch The word secant comes from the Latin word secare meaning to cut.

4. Angles formed by Secants & Tangents When dealing with angles and circles, the vertex can be: ON the circle IN the circle or OUTSIDE the circle **To Help you with this concept you may use three different colored pencils and a clear page protector.

5. Case 1 � Vertex in ON the circleTheorem 9-11 Secant & Tangent intersect

6. Case 2 � Vertex is INSIDE the circle Theorem 9-12 m angle = � the SUM of the intercepted arcs

7. Case 3 � Vertex is OUTSIDE the circle m angle = � the DIFFERENCE of the intercepted arcs

8. Theorem 9-13If two secants, a secant and a tangent, or two tangents intersect in the exterior of the circle, then the measure of the angle formed is one- half the positive difference of the measure of the intercepted arcs.

9. Real-Life Example Tangent-Tangent Angle Two sides of a fence built around a circular pool are shown. The fence touches the pool at points R and M and m of the arc RM = 110. Find the measure of the angle where the two sides of the fence meet, ?RZM. To find m?RZM, you need to know the measure of arc MAR

10. Your assignment