11.1: Tangent lines

1. 11.1: Tangent lines 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

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

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. A B x° 42° C

7. Find x. Assume AB is tangent to the circle. A B 60° x° 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? A 7 24 27 B

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