Practice with Angles in Circles
- Angles Outside the Circle
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Solve the following problems dealing with angles in circles.

(Do not assume diagrams are drawn to scale.)

1.

Given two secants with one going through the center of the circle, find x.

Choose:

20
30
60
80




 

2.

Given two secants, find x.
Hint:  find y first.

Choose:

40
60
80
140



 

3.

Given two tangents,
find x.
 

Choose:

80
100
180
260

 

 

4.

Given a tangent and a secant going through the center of the circle, find x.

Choose:

135
90
55
45

 

 

5.

Given two secants,
find x.   

Choose:

40
70
110
150

 

 

6.

Given two secants,
find x.   

Choose:

105
80
45
25

 

 

7.

Given a tangent and a secant, find x.     

Choose:

135
150
160
180

 

 

8.

Given two tangents,
find x.     

Choose:

30
60
120
180

 

 

9.

Given two secants,
find x.     

Choose:

10
20
30
40

 

 

10. In which of the following diagrams is <1 NOT always equal to <2?

Choose:

                                                                          
 
                   

 

 

11.

From point P outside of a circle, two secants, , are drawn.  Angle P contains 32°, and minor arc    contains 50°.   Find the number of degrees in minor arc .

Choose:

64
84
104
114

 


 

12. Point P lies outside circle O, with diameter .  The angle formed by tangent and secant measures 30°.  Find the measure of minor arc .                       

Answer



 

13. A ferris wheel is being illuminated by a spotlight for evening entertainment.  The spotlight is located such that a light beam strikes the wheel tangent at the points A and B.  A light beam also goes through the center of the wheel, O.   The , BC = 60 meters, and EC = 43.6 meters.

Find the measure of the angle between the light beams and .

Find the diameter of the ferris wheel to the nearest meter.

Answer