1. AB is tangent to circle O at B. The diagram is not drawn to scale.
If AB=7 and AO=17.4, what is the length of the radius (r)? Round to the nearest tenth.
A. 18.8
B. 15.9
C. 12.2
D. 10.4
2. JK, KL, and LJ are all tangent to circle O. The diagram is not drawn to scale.
If JA= 13, AL=19, and CK=7, what is the perimeter of JKL?
A. 39
B. 40
C. 64
D. 78
WZ and XR are diameters of circle C. The diagram is not drawn to scale.
Angle 1= 92°
Angle 2= 50°
What is the measure of ZWX?
A. 322°
B. 230°
C. 272°
D. 38°
4. The radius of circle O is 32, and OC=13. The diagram is not drawn to scale.
What is the length of AB? Round the answer to the nearest tenth.
A. 29.2
B. 34.5
C. 58.5
D. 69.0
5. Circle O is shown below. The diagram is not drawn to scale.
Angle 1=67°
What is the measure of angle BAC?
A. 134°
B. 113°
C. 56.5°
D. 33.5°
6. AC is tangent to circle O at A. The diagram is not drawn to scale.
Is mBY=64°, what is mYAC?
A. 96°
B. 128°
C. 26°
D. 58°
7. In the circle, mBC=62°. The diagram is not drawn to scale.
What is mBCP?
A. 164°
B. 98°
C. 82°
D. 31°
8. The farthest distance satellite signal can directly reach, is the length of the segment tangent to the curve of the Earth’s surface. The diagram is not drawn to scale.
If the angle formed by the tangent, satellite signals is 126°, What is the measure of the intercepted arc on Earth?
A. 252°
B. 108°
C. 63°
D. 54°
9. A circle with two chords is shown below. The diagram is not drawn to scale.
Angle 1= 6
Angle 2= 14
Angle 3= 26
What is the value of x? Round the answer to the nearest tenth.
A. x= 60.7
B. x= 156.0
C. x= 3.2
D. x= 11.1
10. In circle O, BC=14 and DC=25. The diagram is not drawn to scale.
What is the length of diameter BA? Round the answer to the nearest tenth.
A. 58.6
B. 12.2
C. 44.6
D. 30.6
11. A manufacturer is designing a two-wheeled cart that can maneuver through tight spaces. On one test model, see wheel placement (center) and radius are modeled by the equation (x+2)^2 +(y-0.5)^2 =16. Which graph shows the position and radius of the wheels?
12. AB is tangent to circle O at A. The diagram is not drawn to scale.
If AO=21 and BC = 14, what is AB?
A. 21
B. 28
C. 35
D. 42
13. A circle with radius x is shown below. The diagram is not drawn to scale.
Angle 1= 21
Angle 2= 5
What is the value of x? Round the answer to the nearest tenth.
A. x=11.6
B. x=20.4
C. x=15.5
D. x=21.6
14. Circle O is shown below. The diagram is not drawn to scale.
If mR=28°, what is mO?
A. 14°
B. 28°
C. 56°
D. 112°
15. In the circle, AB=19, BC=10, and CD=5. The diagram is not drawn to scale.
What is the value of x?
A. x=23
B. x=53
C. x=38
D. x=58
16.
a. Find x. The figure is not drawn to scale.
b. Is the triangle equilateral, isosceles, or scalene? Explain.
Side 1= (8x-10)°
Side 2= (6x)°
Side 3= (10x+10)°
17. The equation (x+6)^2 + (y+4)^2 =36 models the position and range of the source of a radio signal. Describe the position of the source and the range of the signals.
18. A diameter of a circle has endpoints P(-10, -2) and Q(4, 6).
a. Find the center of the circle.
b. Find the radius. If your answer is not an integer, express it in radical form.
c. Write an equation for the circle.
1. B. 15.9
2. A. 39
3. B. 230°
4. C. 58.5
5. B. 113°
6. C. 26°
7. C. 82°
8. A. 252°
9. A. x= 60.7
10. C. 44.6
11. Graph D
12. B. 28
13. C. x= 15.5
14. C. 56°
15. D. x=58
16.
a. x=7
b. Isosceles, because sides 1 and 3 are congruent
17. The source is located at (-6,-4) and the signals have a range of 6 units in all directions from the center.
18.
a. Center is (-3, 2)
b. Radius is sqrt(65)
c. (x+3)^2 + (y-2)^2 = 65
This was not correct
I apologize for any errors I may have made. Can you please let me know which questions I answered incorrectly so that I can correct them for you?
I got a 5/15
I'm sorry to hear that. May I know which particular questions you would like me to recheck or provide the correct answers for you?
1. To find the length of the radius (r), we can use the fact that AB is tangent to circle O. This means that the radius (r) is perpendicular to AB at the point of tangency (B).
Using the Pythagorean Theorem, we can set up the equation:
r^2 + AB^2 = AO^2
Substituting the given values:
r^2 + 7^2 = 17.4^2
Simplifying:
r^2 + 49 = 302.76
Subtracting 49 from both sides:
r^2 = 253.76
Taking the square root of both sides:
r = √253.76
Rounding to the nearest tenth:
r ≈ 15.9
Therefore, the length of the radius (r) is approximately 15.9. So the answer is B. 15.9.
2. To find the perimeter of JKL, we need to add the lengths of all three tangent segments JK, KL, and LJ.
Given JA = 13, AL = 19, and CK = 7, we can find the lengths of JK, KL, and LJ using the tangent segment theorem.
The tangent segment theorem states that if a line is tangent to a circle, then the lengths of the two tangent segments drawn from an external point to the point of tangency are equal.
So, JK = JA = 13 and LJ = AL = 19.
Now we can add the lengths of all three segments to find the perimeter:
Perimeter = JK + KL + LJ
Perimeter = 13 + KL + 19
Perimeter = KL + 32
Since KL is not given, we cannot directly calculate the perimeter. Therefore, the answer cannot be determined based on the given information.