4.1 Circles 

 

Circle:

A circle is the set of points in a plane that are a fixed distance from a given point. This point is called the center of the circle. To name a circle, use the symbol and the center point. For example, A is read, “circle A.”

Parts of a Circle:

  • Any segment whose endpoints are the center of the circle and a point on the circle is called a radius. In A, the radius is AB
      
        
       
  • Any segment with both endpoints on the circle that PASSES
    through the center is called a diameter.  In A, the diameter is CD
      
        
       
        
  • Any segment with both endpoints on the circle that DO NOT PASS
    through the center is called a chord.  In A, the chord is EF
      
      
      
      
  • All the points within the circle are called the interior of the circle. Points that are not inside the circle and not on the circle are in the exterior of the circle.
      
      
      

Properties of a Circle:

  • The radius "r" of a circle is half the length of the diameter "d"

    r = ½(d)
       
    In G, the radius
     
       
  • The diameter "d" of a circle is twice the length of the radius "r".

    d = 2r
      
     In G, the diameter HI = 2(GH)
      
        
     
  • The circumference of the circle ( distance around the circle ) is equal to the diameter multiplied by π ( pi ≈ 3.14 ).
      
    C = πd    or     C = 2πr    
        
    Note: Use the formula for the information given or needed.

Use this Geogebra app to see the relationship between the Diameter and the Circumference of a Circle

Example A

Task:

Use Geogebra to create A, with radius AB = 4, diameter CD, and chord EF

 

 Solution:

Step:
1.  Plot Point A
2.  Create Circle: Center A & Radius 4
3.  Create Point B, anywhere on the circle.
4.  Create Radius AD ( Segment AD )
5.  Create Point C, anywhere on the circle.
6.  Create Line AC.
7.  Create Point D, at the other intersection of
     line AC and the circle.
8.  Create Diameter CD ( Segment CD )
9.  Create Points E & F, such that Segment EF
     will not go through Point A, then create
     Segment EF
     

You now have A, with radius AB = 4, diameter CD, and chord EF

Press or to run the Geogebra build simulation.








     Watch the video:

 

Quick Question...

Instructions:

  • Use the given "keypad" to enter your answer
  • Click on the "Stopwatch" for a 30 second timer
  • Use the slider to select the numbers of questions

To use the app:

  • Clickto begin, click for full screen mode
  • Clickto check your answer.
  • Clickto goto the next problem
  • Clickto stop the app

  

 

Example B

Question:

What is the circumference of the circle in Example A?

                


Watch the video:
Solution:


 

 

Quick Question...

Instructions:

  • Use the given "keypad" to enter your answer
  • Click on the "Stopwatch" for a 30 second timer
  • Use the slider to select the numbers of questions

To use the app:

  • Clickto begin, click for full screen mode
  • Clickto check your answer.
  • Clickto goto the next problem
  • Clickto stop the app

  

 
 

 

 

Practice Problems

A.  Use Geogebra to create A, with radius AB = 3, diameter CD, and chord BD
      		 
B. What is the diameter of the circle in Practice Problem A?
  
C. What is the circumference of the circle in Practice Problem A?
  
D. What is the radius of a circle with a circumference of 62.8?

     		 

 

Assignment:

1.  Use Geogebra to create A, with radius AB = 4, diameter CD, and chord EF  
   
2.  Use Geogebra to create G, with radius GH, diameter HK = 6, and chord LM
     		 
3.  Use Geogebra to create N, with radius NO, diameter PQ = 7, and chord QR
     		 
4.  Use Geogebra to create S, with radius ST = 2.5, diameter UV, and chord WX
     Make the chord parallel with the radius.
     		 
5.  Use Geogebra to create Z, with radius AZ = 1.5, diameter BC, and chord AB
     Make the radius perpendicular to the diameter.
     		 
6.  In #1, what is the diameter CD = ?
    
7.  In #2, what is the radius GH = ?
  		 
8  In #3, what is the radius NO = ?
  		 
9. In #4, what is the diameter UV = ?
  		 
10.  In #5, what is the diameter BC = ?
   		 
11.  In #1, what is the circumference of  A ?
   		 
12.  In #2, what is the circumference of  G ?
   		 
13.  In #3, what is the circumference of  N ?
   		 
14.  In #4, what is the circumference of  S?
   		 
15.  In #5, what is the circumference of  Z ?
   		 
16.  If the circumference of Q is 12, what is the radius of Q ?
       Round your answer to the nearest hundredth.
     		 
17.  If the circumference of E is 17, what is the diameter of E ?
       Round your answer to the nearest hundredth.
   		 
18.  If the circumference of P is 40.82, what is the radius of P ?
       Round your answer to 2-decimal places.
   		 
19.  If the circumference of H is 7.45, what is the diameter of H ?
       Round your answer to 2-decimal places.
   		 
20.  In #5, what is the length of chord AB ?
      Round your answer to 2-decimal places and show all of your work!