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10.2 Arch and Chords

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10.2 Arch and Chords Powered By Docstoc
					                Bell work
Find the value of radius, x, if the diameter
of a circle is 25 ft.



            25 ft



            x
           Bell work Answer
Radius, x, is 12.5 ft
          Unit 3 : Circles:
       10.2 Arcs and Chords

Objectives: Students will:

1. Use properties of arcs and chords to
solve problems related to circles.
                Words for Circles
 Check your answers to see how you did.
1.    Central Angle
2.    Minor Arc
3.    Major Arc
4.    Semicircle
5.    Congruent Arcs
6.    Chord
7.    Congruent Chords
     Are there any words/terms that you are
     unsure of?
         Label Circle Parts




1.   Semicircles   5. Exterior   9. Tangent
2.   Center        6. Interior   10. Secant
3.   Diameter      7. Diameter   11. Minor Arc
4.   Radius        8. Chord      12. Major Arc
             Arcs of Circles
CENTRAL ANGLE – An angle with its
vertex at the center of the circle
                  Central Angle



                                      A
       CENTER P                   •
                     P
                     •    60º

                                  •   B
                Arcs of Circles
Minor Arc AB and Major Arc ACB
                             Central Angle



                                                 A
          CENTER P                           •       MINOR ARC
                                P
                                                        AB
                                •    60º

  MAJOR ARC              •                   •
                     C                           B
    ACB
                    Arcs of Circles
The measure of the Minor Arc AB = the measure of the Central
Angle
The measure of the Major Arc ACB = 360º - the measure of the
Central Angle             Central Angle



                                              A
            CENTER P                      •       Measure of the
                                                  MINOR ARC =
                               P                  the measure of the
                               •    60º           Central Angle
The measure of the
MAJOR ARC =                  300º
360 – the measure of C   •                •        AB = 60º
                                              B
the MINOR ARC

 ACB = 360º - 60º
     = 300º
                  Arcs of Circles
Semicircle – an arc whose endpoints
are also the endpoints of the diameter
of the circle; Semicircle = 180º

                         180º

                          •

     Semicircle
             Arc Addition Postulate

The measure of an arc formed by two
 adjacent arcs is the sum of the
 measures of the two arcs
                          A
                          •                  •   C

   AB + BC = ABC
                              170º
                                   •   80º
   170º + 8 0º = 2 5 0º



           ARC ABC = 250º
                                       •B
    Example 1



X
•          •
               Y

     75º

    P• 110°



     •
     Z
      Arc Addition Postulate
Answers:

     arcXY  75
     arcYZ  110
     arcXYZ  185
     arcXZ  175
       (p. 605)     Theorem 10.4
In the same circle or in congruent circles
two minor arcs are congruent iff their
corresponding chords are congruent
    Congruent Arcs and Chords
            Theorem
Example 1: Given that Chords DE is
congruent to Chord FG. Find the value
of x.         Arc DE = 100º


           D                        E




            F                   G


                Arc FG = (3x +4)º
   Congruent Arcs and Chords
           Theorem
Answer: x = 32º

               Arc DE = 100º


           D                       E




           F                   G


               Arc FG = (3x +4)º
   Congruent Arcs and Chords
           Theorem
Example 2: Given that Arc DE is
congruent to Arc FG. Find the value
of x.
           D                      E
               Chord DE = 25 in


           Chord FG = (3x + 4) in
            F                   G
    Congruent Arcs and Chords
            Theorem
Answer: x = 7 in



           D                      E
               Chord DE = 25 in


           Chord FG = (3x + 4) in
            F                   G
        (p. 605)        Theorem 10.5

If a diameter of a circle is perpendicular to a chord,
then the diameter bisects the chords and its arcs.

                              Chord


                                            Diameter


      Congruent Arcs            P
                               •

                                            Congruent
                                            Segments
        (p. 605)       Theorem 10.6

If one chord is the perpendicular bisector of another
chord then the first chord is the diameter

                             Chord 2
                                       Chord 1: _|_ bisector
                                       of Chord 2, Chord 1 =
                                       the diameter

                               P
                              •
                                            Diameter
        (p. 606)       Theorem 10.7
In the same circle or in congruent circles, two
chords are congruent iff they are equidistant from
the center. (Equidistant means same perpendicular
distance)

                           Q
                       T
                                   V
Chord TS  Chord QR
    __   __                    •        R
iff PU  VU            U       P


                           S                Center P
              Example
Find the value of Chord QR, if TS = 20
inches and PV = PU = 8 inches

                     Q
                 T
                                    V
                         8 in

                                •       R
                 U            P
                          8 in

                     S                      Center P
             Answer
Chord QR = 20 inches
(Theroem 10.7)
             Home work
PWS 10.2 A

P. 607- 608 (12-46) even
               Journal
Write two things about Arcs and
Chords related to circles from this
lesson.

				
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