1. P DIAMETER: Distance across the circle through its center Also known as the longest chord.

2. P RADIUS: Distance from the center to point on circle

3. Formula Radius = ½ diameter or Diameter = 2r

4. D = ? r = ? D = ?

5. Secant Line: intersects the circle at exactly TWO points

6. a LINE that intersects the circle exactly ONE time Tangent Line: Forms a 90°angle with one radius Point of Tangency: The point where the tangent intersects the circle

7. Name the term that best describes the notation. Secant Radius Diameter Chord Tangent

8. Central Angles An angle whose vertex is at the center of the circle

9. P E F D Semicircle : An Arc that equals 180° EDF To name: use 3 letters

10. THINGS TO KNOW AND REMEMBER ALWAYS A circle has 360 degrees A semicircle has 180 degrees Vertical Angles are CONGRUENT Linear Pairs are SUPPLEMENTARY

11. Formula measure Arc = measure Central Angle

12. m AB m ACB m AE A B C Q 96  E = = = 96° 264° 84° Find the measures. EB is a diameter.

13. Tell me the measure of the following arcs. AC is a diameter. 80  100  40  140  A B C D R m DAB = m BCA = 240  260 

14. Using Properties of Tangents HK and HG are tangent to  F. Find HG. HK = HG 5a – 32 = 4 + 2a 3a – 32 = 4 2 segments tangent to  from same ext. point  segments . Substitute 5a – 32 for HK and 4 + 2a for HG. Subtract 2a from both sides. 3a = 36 a = 12 HG = 4 + 2(12) = 28 Add 32 to both sides. Divide both sides by 3. Substitute 12 for a. Simplify.

15. Applying Congruent Angles, Arcs, and Chords TV  WS. Find mWS. 9n – 11 = 7n + 11 2n = 22 n = 11 = 88°  chords have  arcs. Def. of  arcs Substitute the given measures. Subtract 7n and add 11 to both sides. Divide both sides by 2. Substitute 11 for n. Simplify. mTV = mWS mWS = 7(11) + 11 TV  WS

16. Example 3B: Applying Congruent Angles, Arcs, and Chords  C   J, and mGCD  mNJM. Find NM. GD = NM  arcs have  chords. GD  NM  GCD   NJM Def. of  chords

17. Find QR to the nearest tenth. Step 2 Use the Pythagorean Theorem. Step 3 Find QR. PQ = 20 Radii of a  are . TQ 2 + PT 2 = PQ 2 TQ 2 + 10 2 = 20 2 TQ 2 = 300 TQ  17.3 QR = 2(17.3) = 34.6 Substitute 10 for PT and 20 for PQ. Subtract 10 2 from both sides. Take the square root of both sides. PS  QR, so PS bisects QR. Step 1 Draw radius PQ.

18. The circle graph shows the types of cuisine available in a city. Find mTRQ. 158.4

19. Inscribed Angle Inscribed Angle = intercepted Arc/2

20. 160  80  The inscribed angle is half of the intercepted angle

21. 120  x y Find the value of x and y.    = 120  = 60 

22. In  J, m  3 = 5x and m  4 = 2x + 9. Find the value of x. 3 Q D J T U 4 5x = 2x + 9 x = 3 3x = + 9

23. 4x – 14 = 90 H K G N Example 4 In  K, GH is a diameter and m  GNH = 4x – 14. Find the value of x. x = 26 4x = 104

24. z 2x + 18 85 2x +18 + 22x – 6 = 180 x = 7 z + 85 = 180 z = 95 Example 5 Solve for x and z. 22x – 6 24x +12 = 180 24x = 168

25. 1. Solve for arc ABC 2. Solve for x and y. 244  x = 105  y = 100 

26. Vertex is INSIDE the Circle NOT at the Center

27. Ex. 1 Solve for x X 88  84  x = 100  180 – 88 92

28. Ex. 2 Solve for x. 45  93  xºxº 89  x = 89 360 – 89 – 93 – 45 133

29. Vertex is OUTside the Circle

30. x Ex. 3 Solve for x. 65° 15° x = 25 

31. x Ex. 4 Solve for x. 27° 70° x = 16 

32. x Ex. 5 Solve for x. 260° x = 80  360 – 260 100

33. Warm up: Solve for x 18 ◦ 1.) x 124 ◦ 70 ◦ x 2.) 3.) x 260 ◦ 20 ◦ 110 ◦ x 4.)

34. Circumference, Arc Length, Area, and Area of Sectors

35. Find the EXACT circumference. 1.r = 14 feet 2.d = 15 miles

36. Ex 3 and 4: Find the circumference. Round to the nearest tenths.

37. Arc Length The distance along the curved line making the arc (NOT a degree amount)

38. Arc Length

39. Ex 5. Find the Arc Length Round to the nearest hundredths 8m 70  

40. Ex 6. Find the exact Arc Length. 

41. Ex 7. What happens to the arc length if the radius were to be doubled? Halved? 

42. Area of Circles The amount of space occupied. r A =  r 2 

43. Find the EXACT area. 8. r = 29 feet 9. d = 44 miles

44. 10 and 11 Find the area. Round to the nearest tenths.

45. Area of a Sector the region bounded by two radii of the circle and their intercepted arc.

46. Area of a Sector

47. Example 12 Find the area of the sector to the nearest hundredths. A  18.85 cm 2 60  6 cm Q R

48. Example 13 Find the exact area of the sector. 6 cm 120  7 cm Q R

49. Area of minor segment = (Area of sector) – (Area of triangle) 12 yd R Q Example 14