8 angles inscribed in the same arc 9 congruent chords

8) Angles inscribed in the same arc 9) Congruent chords have congruent _________.
or intercepting congruent arcs are ______________.
x = ______ y = ______ x =
{Cone Head}
10) Two tangent segments from an external point to a circle are ____________.
If AB = 17, x = ______
11) In a circle, parallel chords intercept congruent _________.
x = _____
y = _____
Triple Theorems: if any 2 of the following are true, the third statement is also true.
x
y
78 
110 
x
x
_____
11) a) line through the center of a circle 12) a) line contains the center of a circle
b) line perpendicular to a chord b) line tangent to the circle
c) line bisecting the chord c) line perpendicular at point of tangency
y
100 
70 
x
•
•
A
B
Conclusion: ________________ Conclusion: _____________
•
•
O
M
A
B
O
A
B

Page
25
Circles Worksheet #1
A B C D
1)
A B C D
2)
3)
4)
5)
6)
●
x
30
●
80
x
●
50 y
x
●
x
●
x
y
30
65
110
y
x
x
210
86
x
62
●
x
120
●
x
65
60
x
45
●
50
x
x
150
● 40
x
30
50
x
y
100
x
●
x
2x
y
20
80
x
●
60
x
y
●
50
x
●
100
x
●
50
50
x
y
●
x
20
100
x
30
30

Page
26

Page
27
Circles Worksheet #2
A B C D
1)
A B C
2)
3)
4)
5)
6)
●
80
x
90
120
●
x
280
●
70
x
●
80
x
●
x
100
●
70
x
●
100
30
x
●
x
130
● x
y
80
●
y
x
3y
70
x
●
30
x
●
x
50
●
70
80
x
220
x
110 x
70
x
x
4y
y
●
20
x
100
x
245
●
3y
y
x
●
140
80
x
●
x
120
30
60
80
x

Page
28
Other Angles
1. If mAC = 85 and mDB = 73, then m  1 = _____.
2. If mAD = 136 and mCB = 96, then m  1 = _____.
3. If m  1 = 54 and mAC = 78, then mDB = _____.
4. If m  1 = 48 and mDB = 42, then mAC = _____.
In 5 – 7, EF and EG are tangents.
5. If mFHG = 280, then m  E = _____.
6. If mFG = 96, then m  E = _____.
7. If m  E = 90, then mFHG = ______.
In 8 – 10, IJ is a tangent.
8. If mJK = 120 and mJL = 40, then m  I = _____.
9. If m  I = 45 and mJL = 55, then mJK = _____.
10. If m  I = 50 and mJK = 110, then mJL = _____.
11. If mPT = 100 and mQS = 20, then m  R = _____.
12. If mPT = 130 and mQS = 40, then m  R = ____.
13. If m  R = 25 and mQS = 25, then mPT = _____.
14. If m  R = 40 and mPT = 130, then mQS = ______.
15. If mST = 90, mQS = 60, and mQP = 80, then m  R = _____.
In 16 – 19, DF is tangent to the circle at point E.
16. If mAG = 100 and mBH = 20, then m  C = ______.
17. If m  C = 25 and mBH = 25, then mAG = _____.
18. If mEH = 95 and mGE = 25, then m  D = ______.
19. If m  D = 40 and mEH = 138, then mGE = ______.
A
D
B
C
1
G
E
F

H
K
L I
J
R
Q
P
T
S
A
B
C
D
G
E
F
H
#16 - 19
#11 - 15
#8 - 10
#5- 7
#1- 4

Page
31
Special Segment Notes
Theorem of 2 intersecting chords: When 2 chords intersect inside a circle, the product of the segments of one
chord = the product of the segments of the other chord.
Ex. 1
a • b = c • d x = ______
Ex. 2 Ex. 3
X = _____ x = _____
Theorem of 2 secant segments: When 2 secant segments are drawn from an external point, the product of one
whole secant segment and its external segment = product of the other whole
secant segment and its external segment.
Ex. 1.
(whole secant)( external piece) = (whole secant)(external piece)
X = ________
Theorem of a secant segment and a tangent segment: When a secant segment and a tangent segment are drawn to
Circle from an external point, the product of the whole
Secant segment and its ext. piece = (tangent)
2
.
(whole secant)(ext. piece) = (tangent) 2
Ex1. Ex. 2
X = _____ x = _______
a
b c
d
4
3
x
6
3
x
8
4
•
x x 3
3
4
5
3
x
4
3
x
10
3x
x

Page
32
Special segment lengths in Circles
Solve for x.
1. 2. 3.
x = ________ x = ________ x = ________
4) 5) 6)
x = ________ x = ________ x = ________
7) 8)
x = ________ x = ________
9) 10)
x = ________ x = ________
4
27
6
x
2
9
3
15
2x
x
3x
x
6
•
x
8
2 2.5
8
3
10
x
8
4
x
8
7
x + 3
x
•
4
4
x x
12
27
x
2x - 1
3
x
3x + 4