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12- 2 Chords and Arcs

12- 2 Chords and Arcs. Dawned Pea Hugger Limb Ann. Don't be a girly man. More Circle Properties. R. Chord – A segment whose endpts are on a circle. Ex: PQ. C. P. Central s –  in a circle, whose vertex is at the center of the circle. Rays of central s are radii of the circle .

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12- 2 Chords and Arcs

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  1. 12- 2 Chords and Arcs Dawned Pea Hugger Limb Ann Don't be a girly man

  2. More Circle Properties R • Chord – A segment whose endpts are on a circle. • Ex: PQ C P • Central s –  in a circle, whose vertex is at the center of the circle. • Rays of central s are radii of the circle . • Sum of central s (w/ no common interior pts) are 360° Q

  3. More Circle Properties Thm12-4  Central s have  chords.  Chords have  Arcs.  Arcs have  Central s. A What can you say about arc AB and arc AC? B O C

  4. 12. 2 Chords and Arcs Thm 12-5 • Chords equidistant from the center are . - If TP  RP, then AB  CD 2)  chords are equidistant from the center. - If CD  AB, then TP  RP Thm 12-5 If 1 & 2 are true, then TP bisects AB & RP bisects CD. - If AT  BT, then CR  DR A T ll B ll P C ll ll R D

  5. Ex.2: Solve for the missing Variables mB = 32 12. 2 Chords and Arcs AB = mP = m1 = m2 = BP = 25cm 148 74 74 15.4cm <1 A l l 9cm 16 P B 16 l a2 + b2 = c2 92 + 12.52 = BP2 81 + 156.25 = BP2 BP = 15.4cm l 12.5cm D <2

  6. Thmn 12-6 In a circle, a diameter that is  to a chord bisects the chord & its arc. Thm 12-7 In a circle, a diameter that bisects a chord (that is not a diameter) is  to the chord. Thm 12-8 In a circle, the  bisector of a chord contains the center of the circle. 12. 2 Chords and Arcs

  7. Ex.4: Solve for the missing sides. 12. 2 Chords and Arcs BC = AB = AD = 7m 14m 7.6m A 7m 3m C D a2 + b2 = c2 32 + 72 = AD2 9 + 49 = AD2 AD = 7.6m B

  8. 12-2 HW pg.673 #1,2,3-5,10,11,13,14,18,30,32 pg. 580# 7-9 12. 2 Chords and Arcs Ease Ace Life Ox He's a sly fox

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