Download 8.3: Properties of Angles in a Circle

Circle Geometry
Circumference
 The entire outside of a circle…duh.
Arcs: Major and Minor
 A section of the circumference
is an arc.
 The shorter arc AB is the minor
arc.
 The longer arc AB is the major
arc.
A
B
Central vs Inscribed Angles
 The angle formed by
joining the endpoints of
an arc to any point on a
circle is an inscribed
angle. <ACB
 The angle formed by
joining the endpoints of a
circle to the centre of a
circle is a central angle.
<AOB
C
O
A
B
Inquiring Minds…
 http://staff.argyll.epsb.ca/jreed/math20p/circles/inscribed
_central.htm
Central vs Inscribed Angles
 The inscribed angle is
always half the central
angle OR the central
angle is always double
the inscribed angle.
C
 2(<ACB) = <AOB
O
OR
 <ACB = .5(<AOB )
A
B
Central vs Inscribed Angles
 If <AOB is 80° then
what would <ACB be?
C
 If <ACB is 35° then what
would <AOB be?
O
A
B
A
E
B
I
T
Inscribed Angle Properties
http://staff.argyll.epsb.ca/jreed/math20p/circles/inscribed_inscribed.htm
Inscribed Angle Properties
 So…
 <BET = <BAT = <BIT
A
E
B
I
T
Inscribed Angle Properties
 So what would angles
y° and x° be?
 What circle properties
are we using?
Inscribed Angle Properties
 Inscribed Angles with the
same endpoints are
identical…
 So <ACB = <ADB so angle
x° = 55°
 And a central angle is
double the inscribed
angle with the same
endpoints
 So <ADB x2 = <AOB so
angle y° = 110°
Inscribed Angle Properties
 #1 Inscribed Angles with
the same endpoints are
identical, and #2 a
central angle is double
the inscribed angle with
the same endpoints.
 Remember: The interior
angles of a circle total
360°.
Inscribed Angle Properties
 Where can we start?
 Solve x°? y°? z°
 What could we do to
start filling in the angles?
Here’s our angle bank:
50°
120°
60°
70°
30°
40°
40°
30°
20°
20°
Step 1: 2 different Radii
Where do we start? What would be step #1?
Step 1: 2 different Radii
18
Step 2: Determine QA
18
Step 2: Determine QA
18
33.94
Step 2: Determine PA
18
33.94
Step 2: Determine PA
18
33.94 16.97
Step 1: Determine y
33.94 16.97
Step 1: Determine y
16.97
33.94 16.97
Assignment Time
 Pg. 410:
 3-6, 11, 12, 15