Circles and Arcs
LESSON 10-6
Additional Examples
A researcher surveyed 2000 members of a club to
find their ages. The graph shows the survey results. Find
the measure of each central angle in the circle graph.
Because there are 360° in a circle,
multiply each percent by 360 to
find the measure of each central angle.
65+ : 25% of 360 = 0.25 • 360 = 90
45–64: 40% of 260 = 0.4 • 360 = 144
25–44: 27% of 360 = 0.27 • 360 = 97.2
Under 25: 8% of 360 = 0.08 • 360 = 28.8
HELP
Quick Check
GEOMETRY
Circles and Arcs
LESSON 10-6
Additional Examples
Identify the minor arcs, major arcs, and semicircles in . P with
point A as an endpoint.
Minor arcs are smaller than semicircles.
Two minor arcs in the diagram have point A
as an endpoint, AD and AE.
Major arcs are larger than semicircles.
Two major arcs in the diagram have point A
as an endpoint, ADE and AED.
Two semicircles in the diagram have
point A as an endpoint, ADB and AEB.
Quick Check
HELP
GEOMETRY
Circles and Arcs
LESSON 10-6
Additional Examples
Find mXY and mDXM in . C.
mXY = mXD + mDY
Arc Addition Postulate
mXY = m
The measure of a minor arc is the
measure of its corresponding
central angle.
XCD + mDY
mXY = 56 + 40
Substitute.
mXY = 96
Simplify.
mDXM = mDX + mXWM
Arc Addition Postulate
mDXM = 56 + 180
Substitute.
mDXM = 236
Simplify.
HELP
Quick Check
GEOMETRY
Circles and Arcs
LESSON 10-6
Additional Examples
A circular swimming pool with a 16-ft diameter will be
enclosed in a circular fence 4 ft from the pool. What length of fencing
material is needed? Round your answer to the nearest whole number.
Draw a diagram of the situation.
The pool and the fence are concentric circles.
The diameter of the pool is 16 ft, so the
diameter of the fence is 16 + 4 + 4 = 24 ft.
Use the formula for the circumference of a
circle to find the length of fencing material needed.
C= d
Formula for the circumference of a circle
C = (24)
Substitute.
C 3.14(24)
Use 3.14 to approximate .
C 75.36
Simplify.
About 75 ft of fencing material is needed.
HELP
Quick Check
GEOMETRY
Circles and Arcs
LESSON 10-6
Additional Examples
Find the length of ADB in . M in terms of
.
Because mAB = 150,
mADB = 360 – 150 = 210.
length of ADB =
mADB
•2
360
length of ADB =
210
•2
360
r
(18)
Arc Addition Postulate
Arc Length Formula
Substitute.
length of ADB = 21
The length of ADB is 21
HELP
cm.
Quick Check
GEOMETRY