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OB and OT BT AB TS AB and BT T. 8 8n 90 ° RQ, PQ perpendicular. 6. 14. Quadrilateral ABCD. 15 8.0 28. If the center of a circle is (5, -1), find the equation of the line that is tangent to the circle at (12, 3). - PowerPoint PPT Presentation
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1. OB and OT
2. BT
3. AB
4. TS
5. AB and BT
6. T
7. 8
8. 8n
9. 90°
10. RQ, PQ
11. perpendicular
12. 6
13. 6 214. Quadrilateral ABCD
15. 15
16. 8.0
17. 28
• If the center of a circle is (5, -1), find the equation of the line that is tangent to the circle at (12, 3).
• What is the equation of the circle? (You have to find the length of the radius for this one.)
724
4y x
2 25 1 65x y
A. B.
X = __________ X = __________
C. If OD=12 and CE=10, find DE. A. 68
B. 70
C. 2 85
1. 90 2. 135 3. 135 4. 225
5. 45 6. X=55 7. 20
• Find the center of the circle that passes through the points (-8, -8), (0, -4),
and (-1, -7).
• Find the equation of the same circle
The center is (-5, -4)
2 25 4 25x y
• You are at the very top of a Ferris wheel looking 100 feet down to the ground. If you travel around 10 times, how far have you traveled? Give the exact and approximate distance.
• If your ride took 7 minutes, approximately how fast were you going in feet per minute? Miles per hour?
1000 feet or 3141.59 feet
448.799 feet per minute or 5.1 miles per hour
A.
B.
A. 24
B. 14
30
20
15
90
40
98
B.
A.
75
80
85
56
62
124
6.
90
105
90
50
100
40
• Find the center of the circle that passes through the points (-3, 2), (2, 7),
and (5, -2).
• Find the equation of the same circle
2 22 2 25x y
The center is (2, 2)
1. Arc ZW= Arc XY
4. mZX=mWY
2. Addition property of equality
3. Arc addition postualte
5. Division property of equality
6. Inscribed angle conjecture
7. Substitution
79
64
30
54
100
84
270
40
145
10
40
45
75
50
35
40
75
35
58
90
65
30
30
• If the center of a circle is (1, 4), find the equation of the line that is tangent to the circle at (5, 5).
• What is the equation of the circle? (You have to find the length of the radius for this one.)
2 21 4 17x y
4 25y x
75
105
90
52.5
68 60
65 115 95
First, construct the perpendicular bisectors for each side. Where they cross is the circumcenter. The distance from the circumcenter to a vertex is the length of the radius.
First construct the angle bisectors of each angle. Where they intersect will be the incenter. The distance from the incenter to a side is the length of the radius.
First, draw radius PX. The tangent line will be perpendicular to the radius.
12
12
88
43
12 2
81 100 98
99 40 30
65 29 43
4. Chord 5. Secant 6. Radius 7. Tangent 8. Inscribed 9. Major arc 10. AB=BC
11. 90 degrees
125
235
90
55
40
180
220
TU
13
1. 90 2. 290 3. 55 4. 108 5. 140 6. 20 7a. 105, 75
7b. Its opposite angles are supplementary 8. 140 9. 20
10a. <IHJ
132
48
75
8
52
132
49
12
7 2 21
50
10
Diameter RT perp. To SU – given
<SAT and <UAT are right – def. of perp.
<SAT is congruent to <UAT – right angles are congruent
SA is congruent to UA – a line that is perpendicular to a chord and goes through the center of the circle bisects the chord
AT is congruent to AT – reflexive property
Triangle SAT is congruent to triangle UAT – SAS
ST is congruent to TU – CPCTC
A
A. X = __________
B. X = __________
29
65
Find the value of x and y if O is the center of the circle.
Y=45X=22.5
