Expert: Ahmed Salami - 12/8/2004

Question
A regular hexagon is inscribed in a circle. What is the ratio of the length of a side of the hexagon to the minor arc that it intercepts?
(1) pi/6
(2) 3/6
(3) 3/pi    (This is the correct answer.)
(4) 6/pi
I found the length of the minor arc to be (pi)(r)/3 by doing a sixth of the circumference(2pi r).But I can't find the length of the radius to finish off the problem. If I knew the radius I would then plug it into the above and then use the radius again to be the length of the side because the triangle(one of the six of a hexagon) is equilateral. But can you show me how to get the radius to be 3? Thank you so much.


Answer
Hi Carly,
Really sorry for the delay, i am having my exams and doing a project study at the moment.
You're right about everything, infact you've solve the problem by realising that the length would be just equal to the radius. You need not know what the radius is, its just r.
The ratio would then be
r / (#r/3) = 3/#
I hope you now figure it out. Always happy to help.
Regards.