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

LeoIsTheBest Aug 12, 2019

#2**+3 **

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

LeoIsTheBest Aug 12, 2019

#6**0 **

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

ElectricPavlov Aug 12, 2019