7'2 Discovering Chord Properties

1
7.2 Discovering Chord Properties

• Geometry CP

2
Construction

• With a compass, construct a large circle
• Mark the center, O
• Construct two congruent chords, using a compass
  and a straight edge. Label the chords AB and CD
• Construct radii OA, OB, OC and OD
• Measure the two central angles

Compare your results with your neighbor - can
you make any observations about the angles?
3
Conjecture

• C-61
• If two chords in a circle are congruent, then
  they determine two central angles that are
  congruent

__
__
A
C
O
B
D
4
(
mAB 50
o

• The measure of a central angle is congruent to
  the measure of its intercepted arc.

5
Conjecture

• C-62
• If two chords in a circle are congruent, then
  their intercepted arcs are congruent

6
Construction

• Construct a large circle and mark the center
• Construct a chord that does not pass through the
  center
• Construct a perpendicular to the chord, that
  passes through the center
• Measure both parts of the chord

7
Conjecture

• C-63
• The perpendicular from the center of a circle to
  a chord is the perpendicular bisector of the chord

8
Construction

• Using the previous construction
• Construct a chord congruent to the first chord
• Construct the perpendicular that passes through
  the center
• Measure the distance from the center to both
  chords

9
Conjecture

• C-64
• Two congruent chords in a circle are equally
  distant from the center of the circle

a

a

10
Construction

• Construct a large circle and mark the center
• Construct two nonparallel chords that are not
  diameters
• Construct the perpendicular bisector of each
  chord and extend the bisectors until they
  intersect

11
Conjecture

• C-65
• The perpendicular bisector of a chord passes
  through the center of a circle

12
Homework

• Pages 335-336
• 1-7
• 9-13
• 16
• 19-20