1965 AHSME Problems/Problem 2
A regular hexagon is inscribed in a circle. The ratio of the length of a side of the hexagon to the length of the shorter of the arcs intercepted by the side, is:
Solution
Suppose that each side of the hexagon is . Then the distance from each vertex of the hexagon to the center is also
, so that the circle has radius
. Since the circle has circumference
, the arc intercepted by any side (which measures
) has length
, so that our answer is
and we are done.
See also
1965 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
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