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1.
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Given: AC = 12, AB = 4, EB = 6
Find: ED
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2.
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Given: circle C has radius 7"
arc
AB = 60°
 tangent at A
Find: all  s, arcs, segment lengths, and arc lengths
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3.
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Given:  tangent at T
arc
QT = 80°
AXT = 70°
arc
RT = 110°
Find: all s and arcs
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Answers
(don’t peek until you have tried to solve the problems!)
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1.
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Reasoning:
Since BC = 8, (AB)(BC) = 32.
Thus (EB)(BD) = 32 also.
Since EB = 6, BD =  .
To get ED, use EB + BD as follows:
EB + BD =  .
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2.
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1. AC = BC = EC = 7 in.
2. CAX = 90°
3. arc AB = 60°
4. length of arc AB =  in.
5. ACB = 60°
6. ACE = 120°
7. arc EA = 120°
8. length of arc AE =  in.
9. lower arc EB = 180°
10. length of lower arc EB = 7 in.
11. X = 30°
12. CX = 14 in.
13. BX = 7 in.
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Reasons (numbered only for clarity; this is not a proof):
1. Given
2. Radius to pt. of tangency
3. Given
4.  of circumf. =  , r = 7
5. Central
6. Supp.
7. Based on central ACE
8.  of circumf. (similar
to step 4)
9. Semicircle since C is ctr.
10. Half of circumf., circumf. as above
11. Sum to 180°
12. Double AC since 30°-60°-90°
13. Subtr. (CX minus radius)
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3.
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1. AXT = SXR = 70°
2. SXQ = RXT = 110°
3. arc TR = 110°
4. arc SQ = 110°
5. arc QT = 80°
6. ATX = 95°
7. A = 15°
8. arc SR = 60°
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Reasons (numbered only for clarity; this is not a proof):
1. Given, vert.
2. Supp., vert.
3. Given
4. Must be same since RXT is “Half S”
5. Given
6. Inscr. must be  (arc SQT) = (190°)
7. 180° in AXT, or use (110° – 80°)
8. Use algebra: 70° = (80° + arc SR). Or,
subtract all known arcs from 360°.
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