Chapter 12-3 Properties of Chords _amp; Arcs

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Chapter 12-3 Properties of Chords _amp; Arcs Powered By Docstoc
					       Chapter 12-3
Properties of Chords & Arcs
 Objective:
 • To find the lengths of chords and measures
   of arcs of a circle.
 • To locate the center of a circle using chords.


                 Ms. Chew Geometry 1B               1
           Congruent Arcs & Chords

                   Arc
           P
                               Chords are segments with
               O    Q          endpoints on a circle.

chord PQ




                    Ms. Chew Geometry 1B                  2
• Theorem 12-5
  In the same circle or in congruent circles, (1) congruent central
  angles have congruent arcs; & (2) congruent arcs have congruent
  central angles.

• Theorem 12-6
  In the same circle or in congruent circles, (1) congruent chords have
  congruent arcs; & (2) congruent arcs have congruent chords.


• Theorem 12-7
  A diameter that is perpendicular to a chord bisects the chord and its
  arc.
                          Ms. Chew Geometry 1B                        3
            Chord CE is 24 in. long and 5 in. from the
            center of      A.

Find the radius of      A.
        1
   TC =  24   12
        2                                        A
                                                     5in.
   AC2  52  122                       C                   E
                                                 T
   AC2  169                             24in.
   AC = 13in



                      Ms. Chew Geometry 1B                      4
                    Find mCE

1
  mCE  mCD                                  A
2
                                                 5in
mCE  2mCD                           C       T
                                                       E
mCD  mCAT                           12in   D



mCE  2mCAT                     mCAT  67.380135
          12
tan CAT   2.4                 mCE  2  67.380135 
           5
                                 mCE  134.8
                   Ms. Chew Geometry 1B                    5
Chord BT is 30in. long and 6in. from the
center of   S.

Find the radius of   S.




 Find mBT




                          Ms. Chew Geometry 1B   6
Find the radius of      C to the nearest tenth.
Find mAB to the nearest tenth.

                                          7
                                    S             E
                                         22




             Ms. Chew Geometry 1B                     7
   Questions?
     Complete 12-3
in your homework packet




      Ms. Chew Geometry 1B   8

				
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