M—06/01/09—HW #75: Pg 654-655: 1-20, skip 9, 16. Pg 821-822: 16—38 even, 39— 45 odd 2) C4)...
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Transcript of M—06/01/09—HW #75: Pg 654-655: 1-20, skip 9, 16. Pg 821-822: 16—38 even, 39— 45 odd 2) C4)...
M—06/01/09—HW #75: Pg 654-655: 1-20, skip 9, 16. Pg 821-822: 16—38 even, 39—45 odd2) C 4) B 6) C 8) A 10) 5 12) EF = 40, FG = 50, EH = 24014) (3\2, 2); (5\2) 18) BC, DC 20) BH = 106, HD = 74
16) 35 18) 125 20) 90 22) 9024) 65 26) x = 80, y = 100 28) 9030) 40 32) 46 34) 3 36) 2538) 6
Chapter 10 Review
• Angles – Middle Same
• Inside – Add, div 2
• On – Half
• Outside, subtract, div 2
• Segments – Tan congruent
• Inside, part part = part part
• Outside, part whole = part whole pr
• Part whole = whole squared
PBPAThen
O o tangent tare PB,PA :Given
P
Theorem 10.3
Tangents to a circle from a point are congruent.
O
A
B
A
B C
DE
F
______
___________
___________
||
40,45:
mED
mFDmFBD
mEFDmFD
Find
BCED
EAFmDBCmGiven
Also state if they are major or minor arcs
W
R
NG
O
Theorem 10.4
In the same circle or in congruent circles:
1) Congruent arcs have congruent chords.
2) Congruent chords have congruent arcs.
B
A
N
E
R
Theorem 10.5
A diameter that is perpendicular to a chord bisects the chord and its arc.
Theorem 10.6
If one chord is a perpendicular bisector of another chord, then the first chord is a diameter.
B
A
N
E
R
Theorem 10.7
In the same circle or in congruent circles.
1) Chords equally distant from the center (or centers) are congruent.
2) Congruent chords are equally distant from the center (or centers)
Remember, shortest distance means perpendicular.
45
x
y
z
chords bisectsdiameter
4x
segmentscongruent
npythagorea Some
3y
congruent.
aret equidistan Chords
8z
Def: An inscribed angle is an angle whose vertex is on the circle and sides are chords in the circle.
Theorem: Measure of inscribed angle is half the measure of the intercepted arc.
halfinsc
45
5.22
Look at the pictures, what can you conclude?
12
1
12
3
4
Two inscribed angles intercept same arc, then they are congruent
21
Angle inscribed in semi circle is 90 degrees
Proof: 180\2
901m
If quadrilateral is inscribed in circle, opposite angles supplementary
supp3,2
supp4,1
arcsameinsc 90semiinsc supoppquadinsc
80
angle
whole
xy
zsup
100
angleoppquadinsc
90
90
semiangleinsc
90
90
semiangleinsc
Theorem 10-12
Measure of angle formed by chord and tangent is half the intercepted arc
Chord tan half arc
45
5.22
1
Thrm: Measure of angles formed by two chords that intersect inside the circle is equal to half the sum of the measures of the intercepted arcs.
A
B
C
D
)(2
11 mCDmABm
26
50
38
x
x
x
y
y
y
1
2
3
The measure of an angle formed by two secants, two tangents, or a secant and tangent drawn from a point OUTSIDE the circle is equal to half the difference of the measures of the intercepted arcs.
x y1m )(2
1
x y2m )(2
1
x y3m )(2
1
40
x
30
y
100
z
80, inscribed angle
25, .5(80-30)
50, .5(100-z)=25
80, .5(x+160)=120
40, .5(160-80)=y
120xy
160
10.15 Two chords intersect inside a circle, the product of the segments of one chord equals the product of the segments of the other chord. a
bc
da
bc
d
a
105
30
150=10a
15=a
b
ca
d
Theorem 10.16: When two secants are drawn from an external point, the product of one secant with external segment is equal to the product of the other secant and external segment.
External Segment
Theorem 10.17: When a secant and tangent are drawn to a circle from an external point, the product of the secant and its external segment is equal to the tangent square.
b
a c
ab=cd
ab=c2
A
B
C
D
F
E
?
6?
1012
FE
BFBC
CDAB
8
18
6
816
ECxED
EBAD
4 or 12
A
B
C
D
E
124
)12)(4(0
48160
4816
68)16(
2
2
xorx
xx
xx
xx
xx
Graphing a circle, give radius, center
(x – 3)2 + (y + 1)2 = 25
(h,k) is the center
r is the radius1)Plot center
2) Find radius
3) Plot points
4) Connect
(3,–1)
525
Write equation given center and radius
(x – 2)2 + (y + 4)2 = 21
(2,–4)
21
1) Center
2) Radius
(x – 2)2 + (y –(– 4))2 =( )2
(x + 1)2 + (y – 2)2 = 9
(–1,2)
3
1) Center
2) Radius
(x – (– 1))2 + (y – 2)2 = 3221
• M—06/01/09—HW #75: Pg 654-655: 1-20, skip 9, 16. Pg 821-822: 16—38 even, 39—45 odd
•