Download 12.2 Properties of Arcs

12.2 Properties of Arcs
Geometry
Chapter 12 Circles
The Ferris wheel on the lower right has equally spaced seats, such that
the central angle is 20. How many seats are on this ride? Why do you
think it is important to have equally spaced seats on a Ferris wheel?
Circle – Set of all points
equidistant from a given point
T
** 360°
C
Center
** Name the circle by its center.
D
C
R
Diameter – A segment that contains the center of a circle &
has both endpts on the circle.
Ex. TR
Central Angle – Is an  whose vertex is the center of the
circle.
Ex. TCD
Finding measures of Central s
B
mBAE =
= 40% of 360
= (.40) • 360
25%
A
C
40%
mCAD =
8%
D
= 144
8% of 360
27%
(.08)(360) = 28.8
E
mDAE =
27% of 360 = 97.2
More Circle terms
Arc – Part of a Circle.
* Measured in degrees °
Minor Arc – Smaller than a
semicircle. (< 180°)
R
S
* Named by 2 letters
* Arc Measure = measure
of central 
P
* Ex: RS
Major Arc – Greater than a
semicircle. (> 180°)
* Name by 3 letters
Semicircle – Half of a Circle.
* Order matters
* Name by 3 letters
* Ex: RTS
* Measure = Central 
* Ex: TRS = 180
T
Just like angles, you can add arcs.
B
C
Adjacent Arcs – Are
arcs of the same circle
that have exactly one
point in common.
Ex: AB and BC
A
Arc Addition!!
mBCA = mBC + mCA
Example: Finding the measures of Arcs
B
C
32°
58
mBC = mBOC = 32
32
D
O
mDB = mBC + mCD
= 32 + 58 = 90
mAD = mADC – mCD
148°
122°
A
= 180 – 58 = 122
mAB = mABC – mBC
= 180 – 32 = 148
List the congruent arcs in C below. AB and DE are diameters.
• Solution: ACD= ECB because they
are vertical angles. DCB = ACE
because they are also vertical angles.
Are the blue arcs congruent?
• Solution:
• Since the angles have the
same central angle measure
and in the same circle, the
arcs are congruent.
• The two arcs have the same
angle measure because they
have the same central angle.
But since they have different
radii they are not congruent.
Arc Addition Postulate
The measure of the arc formed by two
adjacent arcs is the sum of the measures of
the two arcs.
Find the measure of the arcs in circle A. EB is the
diameter.
Find the measure of the arcs in circle O.