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Unit 3 Circles

Unit 3 Circles. C. Parts of a Circle. Circle – set of all points _________ from a given point called the _____ of the circle. equidistant. C. center. Symbol:. CHORD:. A segment whose endpoints are on the circle. Radius. RADIUS:. Distance from the center to point on circle. P.

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Unit 3 Circles

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  1. Unit 3 Circles

  2. C Parts of a Circle Circle – set of all points _________ from a given point called the _____ of the circle. equidistant C center Symbol:

  3. CHORD: A segment whose endpoints are on the circle

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

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

  6. D = ? 24 32 12 r = ? 16 r = ? 4.5 6 D = ? 12 9

  7. Q R P S T Use P to determine whether each statement is true or false.

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

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

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

  11. Central Angle : An Angle whose vertex is at the center of the circle ACB AB A Major Arc Minor Arc More than 180° Less than 180° P To name: use 3 letters C To name: use 2 letters B APB is a Central Angle

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

  13. THINGS TO KNOW AND REMEMBER ALWAYS A circle has 360 degrees A semicircle has 180 degrees Vertical Angles are Equal

  14. measure of an arc = measure of central angle m AB m ACB m AE A E 96 Q = 96° B C = 264° = 84°

  15. Arc Addition Postulate m ABC = m AB + m BC A C B

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

  17. CONGRUENT ARCS Congruent Arcs have the same measure and MUST come from the same circle or of congruent circles. C B D 45 45 110 A Arc length is proportional to “r”

  18. Warm up

  19. Central Angle Angle = Arc

  20. Inscribed Angle • Angle where the vertex in ON the circle

  21. Inscribed Angle

  22. 160 The arc is twice as big as the angle!! 80

  23. Find the value of x and y. 120  x  y 

  24. J K Q S M Examples 1. If mJK= 80 and JMK = 2x – 4, find x. x = 22 2. If mMKS= 56, find m MS. 112 

  25. Find the measure of DOG and DIG D 72˚ G If two inscribed angles intercept the same arc, then they are congruent. O I

  26. If all the vertices of a polygon touch the edge of the circle, the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.

  27. Quadrilateral inscribed in a circle: opposite angles are SUPPLEMENTARY B A D C

  28. If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle. diameter

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

  30. Example 4 In K, GH is a diameter and mGNH = 4x – 14. Find the value of x. 4x – 14 = 90 H K x = 26 N G Bonus: What type of triangle is this? Why?

  31. Example 5 Find y and z. z 110 110 + y =180 y y = 70 85 z + 85 = 180 z = 95

  32. Warm Up 1. Solve for arc ABC 244 2. Solve for x and y. x = 105 y = 100

  33. Wheel of Formulas!!

  34. Vertex is INSIDE the Circle NOT at the Center

  35. Ex. 1 Solve for x 88 84 X x= 100

  36. Ex. 2 Solve for x. 93 xº 45 89 x = 89

  37. Vertex is OUTside the Circle

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

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

  40. Ex. 5 Solve for x. 260° x x = 80

  41. Tune: If You’re Happy and You Know It • If the vertex is ON the circle halfthe arc. <clap, clap> • If the vertex is INside the circle half the sum. <clap, clap> • But if the vertex is OUTside, then you’re in for a ride, cause it’s half of the differenceanyway. <clap, clap>

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

  43. Circumference & Arc Lengthof Circles

  44. 2 Types of Answers Rounded • Type the Pi button on your calculator • Toggle your answer • Round Exact • Type the Pi button on your calculator • Pi will be in your answer • TI 36X Pro gives exact answers

  45. Circumference The distance around a circle

  46. Circumference or

  47. r = 14 feet d = 15 miles Find the EXACT circumference.

  48. 33 yd Ex 3 and 4: Find the circumference. Round to the nearest tenth. 14.3 mm

  49. 5. A circular flower garden has a radius of 3 feet. Find the circumference of the garden to the nearest hundredths. C = 18.85 ft

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

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