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avatar+140 

Stuart has drawn a pair of concentric circles, as shown. He draws chords AB, BC,... of the large circle, each tangent to the small one. If

 

 Aug 12, 2019
 #1
avatar+140 
+3

It's supposed to say "If

 Aug 12, 2019
 #2
avatar+140 
+3

If measurement of angle ABC=75 degrees, then how many segments will he draw until he reaches his starting point A.

 Aug 12, 2019
 #3
avatar+102399 
+3

See my answer here:

 

 https://web2.0calc.com/questions/help_9450

 

 

cool cool cool

 Aug 12, 2019
 #4
avatar+140 
+2

Thanks, CPhill! :)

 Aug 12, 2019
 #5
avatar+102399 
+1

OK, Leo....!!!!

 

cool cool cool

CPhill  Aug 12, 2019
 #6
avatar+18754 
+1

I come up with the following:

the 75 degree angle between the two first chords is repeated until the endpoint is back to A

the ARC this angle encompasses is  2 * 75 = 150 degrees

Keep adding 150 degree shifts until the endpoint coincides with A:

 

The LCM of 150 and 360 degrees (which will bring us back to A) is 1800

    1800/150 = 12  angles which will require a total of 13 chords to complete

 Aug 12, 2019

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