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 32º, and minor arc    contains 50º.   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 30º.  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