Download 10.2 Measuring Arcs and Angles

10.2 Measuring Arcs and Angles
Then: You measured angles and identified
congruent angles.
Now:
1. Identify central angles,
major arcs, minor arcs,
semicircles and find
their measures.
2. Find arc lengths.
https://encrypted-tbn2.gstatic.com/images?q=tbn:ANd9GcQoQbm-
Central Angle
*Angle whose vertex is the center of a circle
and whose sides are radii.
*Sum of measures of the central
angles of a circle with no interior
points in common is 360.
Example 1: Find Measures
of Central Angles
a. Find the value of x.
1.
2.
Example 1:
b. Find the value of x.
Arcs of a Circle
*Portion of a circle defined by two endpoints.
Measure of:
Minor arc- less than 180 and equal to the measure of
its central angle.
Major arc- greater than 180; Equal to 360 minus
measure of the minor arc.
Semicircle= 180
Example 2: Classify Arcs and
Find Arc Measures
𝐵𝐷 and 𝐴𝐶 are diameters of Circle O. Identify each arc as a
major arc, minor arc or semicircle of the circle. Then find
its measure.
a. m𝐵𝐴
b. m𝐵𝐶
c. m𝐶𝐷
Example 2
d. m𝐴𝐶𝐵
e. m𝐵𝐶𝐷
f. m𝐴𝐷
Congruent Arcs
Example 3: Find Arc Measures
in Circle Graphs
Use the Bicycles Bought circle graph to find:
a. m𝐾𝐿
b. m𝑁𝐽𝐿
Adjacent Arcs
*Arcs in a circle that have exactly
one point in common.
http://ef004.k12.sd.us/ch10no1.gif
Example 4: Use Arc Addition to
Find Measures of Arcs
Find each measure in Circle M.
a. m𝐿𝐼
b. m𝐼𝐾
Arc Length
*Distance between the endpoints
along an arc measured in linear units.
*Part of the circumference of a circle.
Formula:
Length of arc (l) = Measure of arc (x)  2r
360
𝑥
or l =
2r
360
Example 5: Find Arc Length
a. Find length of 𝐴𝐵 to the nearest hundredth.
Example 5
b. Use Circle O to find the length of each arc.
Round to the nearest hundredth.
1. 𝐷𝐸 if r = 2 m
2. 𝐷𝐸𝐴 if d = 7 in
Example 5
3. 𝐵𝐶 if BE = 24 ft
4. 𝐶𝐴 if DO = 3 mm
Example 5
c. Find m𝐴𝐶 of Circle B.
AB = 5.0 cm
𝐴𝐶 = 9.7 cm
B
C
A
Example 5
d. Find the radius of Circle B.
A
𝐴𝐷𝐶 = 14.7 ft
m𝐴𝐷𝐶 = 247
D
B
C
Example 5
e. Find the circumference of Circle B.
m𝐴𝐶 = 80
𝐴𝐶= 5.4 mm
C
B
A
10.2 Assignment
Pages 710-712
#12-42 evens, 43-50 all
Show your work!!!