Geometry Special Angles Inside a Circle
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The Edge
Special Angles Inside a Circle

 

 There are a couple of tricky things 

 about angles and circles that you should know.
 
 Say you have an angle
 that comes from the center of a circle.
 Like this:
 

 

 
 And another angle that comes from the far side of the circle
 to the same points, like this:
 

 

 
 The trick is that the angle that starts at the edge
 is exactly half as big as the angle that starts in the middle!
 
 Example:
 

 

 
 Well, maybe that one wasn't that big a surprise.
 But I bet this next part is ...
 
 The angle that starts from the edge
 doesn't have to start exactly on the other side of the circle.
 It can start ANYWHERE outside the two points!
 

 

 
 That is one of those amazing but true things in math.
 When I first heard about it (about a million years ago)
 I didn't believe it. 
 But it's true.
 
 The next thing we are going to talk about 
 may be even more amazing.
 
 First some info ...
 

 

 Now back to the incredible part.
 
 One of these "from the edge" angles 
 could be drawn like this:
 
 Start with the big angle from the center ...
 

 

 
 Draw a line like this ...
 

 

 
 and a tangent line, like this ...
 

 

 
 The angle that this makes ALSO counts 
 as one of the half as big angles!
 
 Example:

 

 I think that is amazing!
 Remember that the line outside the circle MUST be tangent.
 We can't just draw that other line in anywhere ...
 

 

 

   copyright 2005 Bruce Kirkpatrick

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