Learning Target I can review properties of angles and segments in circles to determine their measure and length Agenda Do Now Embedded Assessment SelfAssess Circles Properties Review Independent Practice ID: 729184
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Review
Circles Review: Properties, Angles and Segments
Learning Target: I can review properties of angles and segments in circles to determine their measure and length.
Agenda:Do NowEmbedded Assessment Self-AssessCircles Properties ReviewIndependent PracticeDebrief/Note Sheet Creation
DO NOW 3/27:
Find the radius BO if AB = 4in and AO = 5 in.Slide2Slide3
Embedded Assessment: Vertigo RoundSlide4
Definitions:
Radii, Chords, and Tangents
A radius is a line segment with one endpoint at the center of the circle and the other endpoint on the circle.A chord
is a line segment with both endpoints on the circleA tangent is a line that touches the circle at one point (the “point of tangency”)
C
DO
RNTSlide5
Property 1: Radius and Tangent
When a radius and tangent meet, it forms a 90˚ angle.
T
O
N
RSlide6
Property 2: Radius
and Chords A radius that is
perpendicular to a chord bisects that chord.
D
O
R
CxxSlide7
Two Chords…
Two congruent
chords are always the same distance from the center.
R
O
D
CxxHSlide8
Property 3: Two
Tangents… Two tangents starting from the same point outside a circle are congruent to the point of tangency.
O
T
N
x
xASlide9
Review
Circles Review: Arcs, Central and Inscribed Angles Slide10
Definition: Arcs
An arc
is the section of the circumference of a circle between two points.
ACOSlide11
Definition:
Central and Inscribed Angles
A central angle is an angle with its vertex at the center of the circle (sides are radii)
An inscribed angle is an angle with its vertex on the circle (sides are chords)
O
C
TN
ISSlide12
Properties:
Arcs, Central and Inscribed Angles
The measure of a central angle is the same as the arc it intercepts.
The measure of an inscribed angle is ½ of the arc it intercepts.
O
C
TIS
75˚75˚40˚20˚Slide13
Review
Circles Review: Angles Formed by Chords, Tangents and SecantsSlide14
Equation 1:
Angles Formed by Chords
The angle formed by 2 chords is ½ of the sum of the two arcs.x = ½(a+b)
b
a
L
MPQOxxSlide15
Equation 2a
: Angles Formed by Secants
Secant – a line that intersects the circle at 2 pointsThe angle formed by 2 secants is ½ the difference of the two arcs.
x = ½(a-b)
ba
LQ
OxPNMSlide16
Equation 2b: Angles
Formed by Tangent and Secant
The angle formed by a tangent and secant is ½ the difference of the two arcs.x = ½(a-b)
b
aAR
O
xPQSlide17
Equation 3:
Angles Formed by Tangents
The angle formed by two tangents is the major arc minus 180.x = a – 180
a
LP
QO
xSlide18
Review
Circles Review: Segment Lengths in Circles
Learning Target: I can review how to solve problems involving segments in circles, arc length, sector area and equations of a circle.
Agenda:Do NowCircles Properties ReviewJeopardy Review GameEmbedded Assessment Debrief/Note Sheet Creation
DO NOW 3/30: Solve for x.Slide19
Chord Segment Length
When two chords intersect, the products of the two segments lengths of each chord are equal.
LA•AQ = MA•AP
L
M
P
QASlide20
Secants Segment Length
The product of the whole secant segment and the
external secant segment of each secant are equal.LP•LM = LQ•LN
Remember! Whole secant • external secant
LQ
O
PNMSlide21
Tangent and Secant Segment Lengths
The product of the whole secant segment and the external secant is equal to the tangent segment squared.
AR•AQ = AP2
A
RO
P
QSlide22
Review
Act. 4.5: Area, Circumference, Sectors and Arc Lengths
Learning Target: I can review and practice arc lengths, sector area and equations of circles to prepare for the unit exam.Slide23
Circumference and Area
The circumference
of a circle is the distance around the outside of the circle.C = 2πr
The area is the space the circle coversA = πr2
OSlide24
Sector and arc length
Arc˚
/
360˚ = fraction of a circleA sector is a fraction of the area Sector area = (arc˚/360 ˚)(πr2)
The arc length is a fraction of the circumference Arc length = (arc˚/360 ˚)(2π
r)
OSlide25
Review
Act. 4.6: Equation of a CircleSlide26
Equation of a Circle
The equation of a circle is made up of 3 parts:
The radius (r)
The center point (h,k)Another point on the circle (x,y)r
2 = (x-h)2 + (y-k)2(h,k)
(x,y)
r