Arcs of a Circle
Arc:
Consists of two points on a circle and all points
needed to connect the points by a single path.
The center of an arc is the center of the circle
of which the arc is a part.
Central Angle:
An angle whose vertex is at
the center of a circle.
Radii OA and OB determine
central angle AOB.
Minor Arc:
An arc whose points are on or between the side
of a central angle.
Central angle APB determines minor arc AB.
Minor arcs are named with two letters.
Major Arc:
An arc whose points are on or outside of
a central angle.
Central angle CQD determines major arc CFD.
Major arcs are named with three letters (CFD).
Semicircle:
An arc whose endpoints of
a diameter.
Arc EF is a semicircle.
Measure of an Arc
 Minor Arc or Semicircle: The measure is the
same as the central angle that intercepts the arc.
 Major Arc: The measure of the arc is
360 minus the measure of the minor
arc with the same endpoints.
Congruent Arcs
 Two arcs that have the same measure are
not necessarily congruent arcs.
 Two arcs are congruent whenever they
have the same measure and are
parts of the same circle or congruent
circles.
Theorems of Arcs, Chords & Angles…
 Theorem 79: If two central angles of a circle (or of
congruent circles) are congruent, then their
intercepted arcs are congruent.
 Theorem 80: If two arcs of a circle (or of congruent
circles) are congruent, then the corresponding central
angles are congruent.
Theorems of Arcs, Chords & Angles…
 Theorem 81: If two central angles of a
circle (or of congruent circles) are congruent,
then the corresponding chords are
congruent.
 Theorem 82: If two chords of a circle (or
of congruent circles) are congruent, then the
corresponding central angles are congruent.
Theorems of Arcs, Chords & Angles…
 Theorem 83: If two arcs of a circle (or of
congruent circles) are congruent, then the
corresponding chords are congruent.
 Theorem 84: If two chords of a circle (or
of congruent circles) are congruent, then the
corresponding arcs are congruent.
If the measure of arc AB = 102º in
circle O, find mA and mB in ΔAOB.
1. Since arc AB = 102º, then AOB = 102º.
2. The sum of the measures of the angles of a
trianlge is 180 so…
1. mAOB + mA + mB = 180
2. 102 + mA + mB = 180
3. mA + mB = 78
3. OA = OB, so A  B
4. mA = 39 & mB = 39.
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Circles P & Q
P  Q
RP  RQ
AR  RD
AP  DQ
Circle P  Circle Q
Arc AB  Arc CD
1.
2.
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Given
Given
.
Given
Subtraction Property
Circles with  radii are .
If two central s of 
circles are , then their
intercepted arcs are .