Re: Two Olympiad Problems
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Here is the way that requires neither geometrical ingenuity nor taking second derivatives of trigonemetric functions. (If Tom Cowley does that again his reign here will be short lived.) Take a string six inches long and attach the ends. Thumbtack a potion of it on a horizontal line.Pull the rest up to make a triangle and notice that it is highest, and thus has greatest area, when it is isosceles.
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Bah. That's exactly the observation I made, except I gave a proof that it was true instead of just stating that it was true.
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