1. OBJECTIVES: STUDENTS WILL BE ABLE TO… USE THE RELATIONSHIP BETWEEN A RADIUS AND A TANGENT USE THE RELATIONSHIP BETWEEN 2 TANGENTS FROM ONE POINT FIND THE MEASURE OF AN ANGLE FORMED BY 2 TANGENTS INTERSECTING OUTSIDE THE CIRCLE 11.1: Tangent lines

2. Warm Up K B C A 85° 1.Name a minor arc and find its measure. 2.Find measure of <ACB.

3. DEFINITION TANGENT TO A CIRCLE: Line in the plane of the circle that intersects the circle at exactly one point. POINT OF TANGENCY: Where the circle and the tangent line intersect

4. THEOREM If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency.

5. Find the value of x. Assume the lines are tangent to the circle. x°110°

6. Find x. Assume the line is tangent. B A C 42° x°

7. Find x. Assume AB is tangent to the circle. B A x° 60° C

8. Theorem If a line in the plane of a circle is perpendicular to a radius at its endpoint on the circle, then the line is tangent to the circle. Line AB is tangent to circle O.

9. Is segment AB tangent to the circle? 24 7 27 B A

10. Is segment AB tangent to the circle? 15 5 16 A B

11. DEFINITIONS A polygon is inscribed in a circle if all vertices of the polygon lie on the circle. A polygon is circumscribed about the circle if each side of the polygon is tangent to the circle.

12. THEOREM The 2 segments tangent to a circle from a point outside the circle are congruent.

13. EXAMPLE: Find x. The lines are tangent to the circle. 17 x

14. Find x 2x+7 21

15. Find the perimeter.

16. You try….find the perimeter.

17. Theorem: The measure of an angle formed by 2 lines that intersect outside a circle is half the difference of the measures of the intercepted arcs. In other words, the measure of angle 1 is…

18. Example: Find x.