Lesson 8-1: Circle Terminology 1
Lesson 10-1
Circle Terminology
Lesson 8-1: Circle Terminology 2
Circle DefinitionCircle : The set of points coplanar points equidistant from a
given point.
The given point is called the CENTER of the circle.
The distance from the center to the circle is called the RADIUS.
Center
Radius
Lesson 8-1: Circle Terminology 3
DefinitionsChord : The segment whose endpoints lie on the circle.
Chord
Diameter : A chord that contains the center of the circle.
DiameterSecant : A line that contains a chord.Secant
Tangent : A line in the plane of the circle that intersects the circle in exactly one point.
Point of Tangency :
The point where the tangent line intersects the circle.
Tangent
Lesson 8-1: Circle Terminology 4
Example: In the following figure identify the chords, radii, and diameters.
, ,AB BF CEChords:
Radii:
Diameter:
O
D
A
B
F
C
EFB
Lesson 8-1: Circle Terminology 5
Circles that have congruent radii.
22
Circles that lie in the same plane and have the same center.
Definitions
Concentric circles :
Congruent Circles :
Lesson 8-1: Circle Terminology 6
CIRCUMFERENCE:Circumference is the distance around the circle.
2C r C d2d r
Formula: Or
Example: Find the circumference of the following circle.
3 cm
2 (3)C6C
18.85C cm
where
Lesson 8-1: Circle Terminology 7
Examples:
1) Find the circumference of a helipad if it has a diameter of 79 feet.
2) Find the circumference of each circle described. Round to the nearest hundredth• a) radius=2.5 cm b) diameter=16ft
Lesson 8-1: Circle Terminology 8
Polygons
A polygon inside the circle whose vertices lie on the circle.
Inscribed Polygon:
Circumscribed Polygon :
A polygon whose sides are tangent to a circle.
Lesson 8-2: Formulas 9
ARCSThe part or portion on the circle from some point B to C
is called an arc.
A
B
C
Arcs :
Semicircle: An arc that is equal to 180°.
Example:
OA
B
CExample: ABC
Lesson 8-2: Formulas 10
Central AngleA central angle is an angle whose vertex is at the center of the circle.
The measure of a minor arc is the measure of its central angle.
The measure of a major arc is 360 minus the measure of its central angle.
The arc measure is written as m BC
mBC m BAC
Central Angle
A
B
CBAC
Lesson 8-2: Formulas 11
Minor Arc & Major Arc
AB
Minor Arc : A minor arc is an arc that is less than 180°
A minor arc is named using its endpoints with an “arc” above.
A
B
Example:
Major Arc: A major arc is an arc that is greater than 180°.
A major arc is named using its endpoints along with another point on the arc (in order).A
B
CExample: ABC
O
Lesson 8-2: Formulas 12
Example: ARCSIdentify a minor arc, a major arc, and a semicircle, given that
is a diameter.
, , ,DE EC CF DF
A
C
D
E
F
Minor Arc:
CD
Major Arc: , , ,CEF EDC DFE FCD
Semicircle: , ,CFD CEDEDF ECF
Lesson 8-2: Formulas 13
Adjacent Arcs
Adjacent arcs-arcs in a circle that have exactly one point in common.
BC and CD are adjacent arcs
Lesson 8-2: Formulas 14
Arc LengthArc length is the distance around an arc.
236072
2 4360
ar
The circumference multiplied by the ratio of the center angle and 360°.
Formula:
Example:
4 cm
72 B
C
A
0.8 2.51 cm
Arc Length
Lesson 8-2: Formulas 15
Examples:
Find the Arc length. Round to the nearest hundredth.
1) 2)