Geometry Circle Properties
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Forget Your Lines
Circle Properties

 

 When we have angles in circles,

 sometimes we draw in the lines ...
 

 

 
 But sometimes we don't.
 WHAT? AN ANGLE WITH NO LINES?
 JUST HOW ARE YOU GOING TO DO THAT???
 
 Easy, like this:
 1) Draw a circle.
 2) Put a point in the center.
 3) Put a point where each line would touch the circle
    if we did draw the lines.
 4) Label the points with letters.
 

 

 
 Now we can say angle BAC.
 Let your mind put in the lines.
 

 

 
 Maybe you can see that Angle BAC 
 is not the same as Angle BCA
 

 

 
 Now we can put together some stuff
 from the last couple of pages ...
 
 Example:
 

 

 
 Angle BEC is 100 degrees.
 What is the measure of angle DAC?
 
 Let's draw in some lines ...
 

 

 
 1) Since angle BEC is 100 degrees, 
 angle AED is also 100 degrees.
 

 

 
 2) All of the angles in the circle add up to 360 degrees.
 Angle AEB and angle DEC are the same as each other.
 

 AEB + 100 + DEC + 100 = 360

AEB + DEC = 160

AEB = 80           DEC = 80

 

 

 
 3) Now we can think about angle DAC.
 Get rid of a few lines and draw a few others ...
 

 

 
 A couple of pages ago we talked about stuff like this.
 Angle DAC and angle DEC end up at the same points.
 Angle DEC starts at the center.
 Angle DAC starts at the edge.
 Angle DEC is 80 degrees 
 so angle DAC is 40 degrees.
 

 

 

   copyright 2005 Bruce Kirkpatrick

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