Day 2 –
Using Arcs of Circles
In a
plane, an angle whose vertex is the center of a circle and whose sides
intersect the circle is a central angle of the circle.
A
central angle separates a circle into arcs.
There are three types of arcs:
Minor
Arc
A
minor arc is part of the circle in the interior of the central angle with
measure less than 180°. In the diagram
above, the measure of the central angle, 
, is less than 180°, then A
and B and the points of Circle C in the interior of form a minor arc of
the circle.
Major
Arc
A
major arc is part fo the circle in the exterior of the central angle. In the diagram, the points A and B and the points of Circle C in the exterior of form a major arc of
the circle.
Semicircle
If
the endpoints of an arc are the endpoints of a diameter, then the arc is a
semicircle.
NAMING
ARCS
Arcs
are named by their endpoints. Major arcs
and semicircles are name by their endpoints and by a point on the arc.
MEASURING
ARCS
Measures
of arcs are related to corresponding central angles.
The
measure of a minor arc is defined to be the measure of its central
angle.
The
measure of a major arc is defined as the difference between 360° and the
measure of fits associated minor arc.
The measure of the whole circle is 360°.
The
measure of a semicircle is 180°.
Two
arcs of the same circle are adjacent
if they intersect at exactly one point.
You can add the measures of adjacent arcs.
ARC
ADDITION POSTULATE
The
measure of an arc formed by two adjacent arcs
is
the sum of the measures of the two arcs.
Two
arcs of the same circle or of congruent circles are congruent arcs if
they have the same measure.