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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).
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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). • What is the equation of the circle? (You have to find the length of the radius for this one.)
B. A. X = __________ X = __________ C. If OD=12 and CE=10, find DE. A. 68 B. 70
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)
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. • 24 • 14 B.
30 20 15 90 40 98
A. 75 80 85 B. 56 62 124
90 105 90 6. 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 The center is (2, 2)
2. Addition property of equality 3. Arc addition postualte 5. Division property of equality 6. Inscribed angle conjecture 7. Substitution 1. Arc ZW= Arc XY 4. mZX=mWY
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.)
90 52.5 75 105
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
100 98 81
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
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
21 50 10
A 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
29 A. X = __________ 65 B. X = __________
Find the value of x and y if O is the center of the circle. Y=45 X=22.5