9.3. Arcs in Circles http://www.ck12.org
CK-12 Foundation: Chapter9ArcsinCirclesB
Concept Problem Revisited
Because the seats are 20◦apart, there will be^360
◦
20 ◦ =18 seats. It is important to have the seats evenly spaced for
balance. To determine how far apart the adjacent seats are, use the triangle to the right. We will need to use sine to
findxand then multiply it by 2.
sin 10◦=x
25
x=25 sin 10◦= 4. 3 f t.The total distance apart is 8.6 feet.
Vocabulary
Acircleis the set of all points that are the same distance away from a specific point, called thecenter. Anarcis a
section of the circle. Asemicircleis an arc that measures 180◦. Acentral angleis the angle formed by two radii
with its vertex at the center of the circle. Aminor arcis an arc that is less than 180◦. Amajor arcis an arc that is
greater than 180◦.
Guided Practice
- List the congruent arcs in
⊙
Cbelow.ABandDEare diameters. - Are the blue arcs congruent? Explain why or why not.
a)
b)
- Find the value ofxfor
⊙
Cbelow.
Answers:
1.^6 ACD∼=^6 ECBbecause they are vertical angles.^6 DCB∼=^6 ACEbecause they are also vertical angles.
AD̂∼=EB̂andAÊ∼=DB̂
- a)AD̂∼=BĈbecause they have the same central angle measure and are in the same circle.
b) The two arcs have the same measure, but are not congruent because the circles have different radii.
- The sum of the measure of the arcs is 360◦because they make a full circle.
mAB̂+mAD̂+mDB̂= 360 ◦
( 4 x+ 15 )◦+ 92 ◦+( 6 x+ 3 )◦= 360 ◦
10 x+ 110 ◦= 360 ◦
10 x= 250
x= 25