Lesson 2 Measuring Arcs and Angles of a Circle
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Last updated 3 months ago
17 Nsɛmmisa
1
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arc
endpoints
minor arc
two
Semicircle
degrees
three
linear units (ie inches)
less than
greater than
major arc
Click on "Show Central Angle
".Look at the vertex (Point O) and the two sides (
and ) of central angle . What can we deduce about central angles?A CENTRAL ANGLE of a circle is an angle whose vertex is the circle and the sides are of the circle.
In Circle O, m
and m, then mIdentify each arc as a minor arc, major arc, or semicircle. Then find its measure.
Arc | Type of Arc | Arc Measure |
|---|---|---|
In Circle O,
.a) Name the minor arcs.
b) Name the major arcs.
c) Name the central Angles
d) Name the central angle that intercepts
e) Name the central angle that intercepts
Minor Arcs
Major Arcs
Central Angles
Central
that interceptsCentral
that interceptsLets Do an Arc length example together
Find the length of an arc of a
in a circle with a radius of 12.Leave answer in terms of
.Find the length of an arc of a
in a circle with a radius of 18.Leave answer in terms of
.Find the length of an arc of a
in a circle with a radius of 10.Leave answer in terms of
.Find the length of an arc of a
in a circle with a radius of 9.Leave answer in terms of
.Find the length of an arc of a
in a circle with a diameter of 56.Leave answer in terms of
.In a circle whose radius is 8, find the number of degrees contained in the central angle of an arc whose length is
.Definitions and Properties of Arcs (GeoGebra Applet )
An is a set of points on the circle consisting of two endpoints and all the points between them.
Arcs can be measured in and/or .
There are three types of arcs:
is an arc which is one of the two arcs into which a diameter divides a circle.
Its measure is .
It is named by using points (first and last points are the and one other point on the arc)
A of a circle is an arc which is smaller than a semicircle.
Its measure is .
It is named by using points (its )
A of a circle is an arc which is larger than a semicircle.
Its measure is .
It is named using points (first and last points are the and one other point on the arc).
In the following slides, you will see that their exist relationships between the measure of the arcs and the angles that intercept them.
Click on "Show
" and "Show Positional Relationship..."Look at where is in relation to central angle
.Which of the following statements correctly depicts the positional relationship between a central angle (
) and its arc ().Click on "Show m
".The measure of an arc is
Example: m
Click on all of the remaining checkboxes.
What is TRUE about ALL of the (non-overlapping) central angles of a circle?
What is TRUE about ALL of the (non-overlapping) arcs of a circle?
In Circle O,
and m.Find:
a) m
b) m
c) m
d) m
