1. 10.1– Use Properties of Tangents of Circles

2. TermDefinitionPicture Circle The set of all points in a plane that are equidistant from a given point

3. TermDefinitionPicture Center Point equidistant from the sides of the circle. Gives the name of the circle. P

4. TermDefinitionPicture Radius A segment with endpoints at the center and on the circle P Q

5. TermDefinitionPicture Chord A segment with both endpoints on the circle P Q A

6. TermDefinitionPicture Diameter A segment with both endpoints on the circle that goes through the center of the circle P Q R

7. TermDefinitionPicture Secant A line that intersects a circle in two points. P Q R

8. TermDefinitionPicture Tangent A line that intersects a circle in exactly one point. P Q R

9. TermDefinitionPicture Point of Tangency The point where a tangent line touches a circle P Q R S S

10. TermDefinitionPicture Common Internal Tangent A line that is tangent inside two circles.

11. TermDefinitionPicture Common External Tangent A line that is tangent outside two circles.

12. TermDefinitionPicture Coplanar Circles Two circles on the same plane

13. TermDefinitionPicture Concentric circles Circles that have the same center

14. In a plane, a line is ______________ to a circle if and only if the line is ____________________ to a radius of the circle and its endpoint on the circle. tangent perpendicular

15. Tangent segments from a common ____________ point are ___________________. externalcongruent A B C

16. 1. State the best term for the given figure. C center

17. 1. State the best term for the given figure. Common internal tangent

18. 1. State the best term for the given figure. radius

19. 1. State the best term for the given figure. chord

20. 1. State the best term for the given figure. Point of Tangency

21. 1. State the best term for the given figure. diameter

22. 1. State the best term for the given figure. secant

23. 1. State the best term for the given figure. Common External Tangent

24. 2. Find the radius of 2u2u

25. 3. Find the diameter of 4u4u

26. 4. Find the center of (2, 4)

27. 5. The points K and M are points of tangency. Find the value of x. x = 22

28. 5. The points K and M are points of tangency. Find the value of x. 4x + 7 = 7x – 8 7 = 3x – 8 15 = 3x 5 = x

29. 6. In the diagram, is a radius of Determine whether is tangent to Explain your reasoning. c 2 = a 2 + b 2 5 2 = 3 2 + 4 2 25 = 9 + 16 25 = 25 Right Triangle Yes

30. c 2 = a 2 + b 2 19 2 = 8 2 + 16 2 361 = 64 + 256 361 > 320 Not a Right Triangle NO 6. In the diagram, is a radius of Determine whether is tangent to Explain your reasoning.

31. 7. Given the picture, find the indicated length. c 2 = a 2 + b 2 80 2 = a 2 + 48 2 6400 = a 2 + 2304 4096 = a 2

32. Given the picture, find the indicated length. c 2 = a 2 + b 2 25 2 = x 2 + 12 2 625 = x 2 + 144 481 = x 2 6

33. Given the picture, find the indicated length. c 2 = a 2 + b 2 (r + 2) 2 = r 2 + 4 2 r 2 + 4r + 4 = r 2 + 16 4r + 4 = 16 4r = 12 r = 3 (r + 2)(r + 2) = r 2 + 16 r 2 + 2r + 2r + 4 = r 2 + 16

34. Given the picture, find the indicated length. c 2 = a 2 + b 2 (r + 9) 2 = r 2 + 15 2 r 2 + 18r + 81 = r 2 + 225 18r + 81 = 225 18r = 144 r = 8 (r + 9)(r + 9) = r 2 + 225 r 2 + 9r + 9r + 81 = r 2 + 225

35. c 2 = a 2 + b 2 (r + 16) 2 = r 2 + 24 2 r 2 + 32r + 256 = r 2 + 576 32r + 256 = 576 32r = 320 r = 10 (r + 16)(r + 16) = r 2 + 576 r 2 + 16r + 16r + 256 = r 2 + 576 10.1655-6573-10, 15-23 odd, 24, 27, 28 HW Problem #21