# Chapter 12-3 Properties of Chords _amp; Arcs by ewghwehws

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```									       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.

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 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