12- 2 Chords and Arcs

Dawned Pea Hugger Limb Ann

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More Circle Properties

C

Q

P

R Chord – A segment whose endpts are on a circle.

•Ex: PQ

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°

Thm12-4 Central s have chords. Chords have Arcs. Arcs have Central s.

More Circle Properties

A

B

C

O

What can you say about arc AB and arc AC?

Thm 12-51)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 TB

P

RD

C

llll

llll

12. 2 Chords and Arcs

Ex.2: Solve for the missing Variables

• mB = 32

A

BP

D

l

l

l

l

9cm

12.5cm

1616

AB =

mP =

m1 =

m2 =

BP =

25cm

148

74

74

15.4cm

a2 + b2 = c2

92 + 12.52 = BP2

81 + 156.25 = BP2

BP = 15.4cm

12. 2 Chords and Arcs

<1

<2

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 diameterthat 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

Ex.4: Solve for the missing sides.

A

B

D C

7m

3m

BC =

AB =

AD =

7m

14m

7.6m

aa22 + b + b22 = c = c22

3322 + 7 + 722 = AD = AD22

9 + 49 = AD9 + 49 = AD22

AD = 7.6mAD = 7.6m

12. 2 Chords and Arcs

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

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