Difference between revisions of "1965 AHSME Problems/Problem 2"
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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: | 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: | ||
Latest revision as of 13:47, 16 July 2024
Problem
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 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
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