1. CIRCLES Unit 9; Chapter 10

2. Tangents to Circles lesson 10.1 California State Standards 7: Prove and Use theorems involving properties of circles. 21: Prove and Solve relationships among chords, secants and tangents. Lesson Goals Identify lines and segments in circles. Give the equation for a tangent line on the coordinate plane. Recognize tangent and concentric circles. ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

3. definitions Circle The set of all points in a plane that are equidistant from a given point. Center The given point. Radius A line segment with the center as one endpoint and a point on the circle as the other endpoint. The distance from the center to a point on the circle.

4. definitions Circle The set of all points in a plane that are equidistant from a given point. Center The given point. Radius A line segment with the center as one endpoint and a point on the circle as the other endpoint. The distance from the center to a point on the circle. C P the plural of radius is radii

5. definitions Congruent Circles Circles with the same radius Diameter A line segment with endpoints on the circle that contains the center of the circle. The distance across a circle through the center. 2 r = d

6. Congruent Circles Circles with the same radius Diameter A line segment with endpoints on the circle that contains the center of the circle. The distance across a circle through the center. 2r = d definitions P C R 2r = d X Y

7. definitions Chord A segment whose endpoints are on the circle. A diameter is a “specialized” chord. Secant A line that intersects a circle in two points. A chord is part of a secant. Tangent A line that intersects a circle in exactly one point. The circle and line must lie in the same plane.

8. Chord A segment whose endpoints are on the circle. A diameter is a “specialized” chord. Secant A line that intersects a circle in two points. A chord is part of a secant. Tangent A line that intersects a circle in exactly one point. The circle and line must lie in the same plane. definitions C A B F G T U

9. radius C P A B Q X diameter chord secant tangent Identify each line or segment chord point of tangency

10. definition Tangent Circles Coplanar circles that intersect in exactly one point. internally tangent circles

11. definition Tangent Circles Coplanar circles that intersect in exactly one point. externally tangent circles

12. definition Concentric Circles Coplanar circles with a common center.

13. definition Common Tangent A line or segment that is tangent to two coplanar circles Common Internal Tangent crosses between the circles Common External Tangent stays along the edges of the circles

14. Common Tangent A line or segment that is tangent to two coplanar circles Common Internal Tangent crosses between the circles Common External Tangent stays along the edges of the circles definition C o m m o n I n t e r n a l T a n g e n t Common External Tangent

15. example Is the common tangent internal or external? external C D T

16. example C H B A I D E F G Describe each segment and line tangent diameter chord radius secant Point of tangency radius

17. definitions exterior interior Interior of a Circle The set of points inside the circle Exterior of a Circle The set of points outside the circle.

18. example What are the coordinates of each center? What is the radius of each circle? x y AB

19. example Describe the intersection of the two circles. x y AB

20. example Describe the common tangents of the circles. x y AB

21. A y example B What are the coordinates of each center? What is the radius of each circle? Describe any common tangents. x

22. 22 Today’s Assignment  p. 599: 10 – 16 e, 18 – 35

23. 10. The diameter of a circle is 6.7 inches. Find the radius. 12. The diameter of a circle is 8 cm. Find the radius. 14. The radius of a circle is 62 ft. Find the diameter. 16. The radius of a circle is 4.4 cm. Find the diameter. #29 - 31 Copy the diagram. Tell how many common tangents the circles have. Then sketch the tangents. Match the notation with the term that best describes it. #26 - 28 Tell whether the tangent(s) are internal or external