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Stuart has drawn a pair of concentric circles, as shown. He draws chords $\overline{AB}$, $\overline{BC}, \ldots$ of the large circle, each tangent to the small one. If $m\angle ABC=75^\circ$, then how many segments will he draw before returning to his starting point at $A$?

 

 Jul 26, 2020
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Each chord goes 2*75 = 150 degrees around the circle.  It will then take 360/150*5 = 12 chords to go around the circle.

 Jul 27, 2020

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