circle basics central angles. definition - circle a circle is the collection of all points in a...
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Circles, ICircle Basics
Central Angles
Definition - CircleA circle is the collection of all points in a
plane equidistant from a given point called the center of the circle.
Definition - CircleA circle is the collection of all points in a
plane equidistant from a given point called the center of the circle. ⨀𝐶
Example – Identify the parts of a CircleName the circleName a radius of the circleName a chord of the circleName a diameter of the circle
Example – Identify the parts of a CircleName the circleName a radius of the circleName a chord of the circleName a diameter of the circle
⨀ 𝐾
Example – Identify the parts of a CircleName the circleName a radius of the circleName a chord of the circleName a diameter of the circle
⨀ 𝐾
KRKQKPKOKNRadii ,,,,:
Example – Identify the parts of a CircleName the circleName a radius of the circleName a chord of the circleName a diameter of the circle
⨀ 𝐾
KRKQKPKOKNRadii ,,,,:
RPNOChords ,:
Example – Identify the parts of a CircleName the circleName a radius of the circleName a chord of the circleName a diameter of the circle
⨀ 𝐾
KRKQKPKOKNRadii ,,,,:
RPNOChords ,:
RPDiameter :
Radius/DiameterBy the definition of a circle, the distance from
the center to any point on the circle is always the same. Therefore, all radii are congruent (have the same measurement)
A diameter is the sum of 2 radii, thus,
rd
rd 2
2
Compute Radius and DiameterCircle A has diameter .
If DF = 10, DA = ?
If PA=7, PG=?
If AG=12, LA=?
Compute Radius and DiameterCircle A has diameter .
If DF = 10, DA = ?
If PA=7, PG=?
If AG=12, LA=?
rd 2
Compute Radius and DiameterCircle A has diameter .
If DF = 10, DA = ?
If PA=7, PG=?
If AG=12, LA=?
rrd 2102
Compute Radius and DiameterCircle A has diameter .
If DF = 10, DA = ?
If PA=7, PG=?
If AG=12, LA=?
rrrd 52102
Compute Radius and DiameterCircle A has diameter .
If DF = 10, DA = ?
If PA=7, PG=?
If AG=12, LA=?
rrrd 52102
rd 2
Compute Radius and DiameterCircle A has diameter .
If DF = 10, DA = ?
If PA=7, PG=?
If AG=12, LA=?
rrrd 52102
)7(22 drd
Compute Radius and DiameterCircle A has diameter .
If DF = 10, DA = ?
If PA=7, PG=?
If AG=12, LA=?
rrrd 52102
14)7(22 ddrd
Compute Radius and DiameterCircle A has diameter .
If DF = 10, DA = ?
If PA=7, PG=?
If AG=12, LA=?
rrrd 52102
14)7(22 ddrd
12LAAG
Example 2The diameter of circle A is 10, circle B 20 and
circle C 14.
Find XB
Find BY
Definition – CircumferenceThe circumference of a circle is the distance
around the circle. Essentially, the perimeter of a circle, denoted by C.
rdC 2
Definition – CircumferenceThe circumference of a circle is the distance
around the circle. Essentially, the perimeter of a circle, denoted by C.
Find C if r = 7.
Find C if d = 12.5
rdC 2
14)7(2 C
Definition – CircumferenceThe circumference of a circle is the distance
around the circle. Essentially, the perimeter of a circle, denoted by C.
Find C if r = 7.
Find C if d = 12.5
rdC 2
14)7(2 C
5.12C
CWAngles & Arcs
Definition – Central AngleA central angle has the center of the circle as
its vertex, and its sides contain two radii of the circle.
Example 1 – Central AnglesCompute the measurement of angle AOD in
circle O.
Example 1 – Central AnglesCompute the measurement of angle AOD in
circle O.180 COBmDOCmAODm
Example 1 – Central AnglesCompute the measurement of angle AOD in
circle O.180 COBmDOCmAODm
1802325 xxx
Example 1 – Central AnglesCompute the measurement of angle AOD in
circle O.180 COBmDOCmAODm
1802325 xxx18030 x
Example 1 – Central AnglesCompute the measurement of angle AOD in
circle O.180 COBmDOCmAODm
1802325 xxx18030 x
30
180
30
30x
Example 1 – Central AnglesCompute the measurement of angle AOD in
circle O.180 COBmDOCmAODm
1802325 xxx18030 x
30
180
30
30x
6x
Example 1 – Central AnglesCompute the measurement of angle AOD in
circle O.180 COBmDOCmAODm
1802325 xxx18030 x
30
180
30
30x
6x
150)6(2525 xAODm
CW 13, part 2