Lion and Man

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A man and a lion are inside a disk of radius 1 with center . Both have a top speed of 1. Can the man choose a strategy to avoid being captured by the lion?
Contributed by: Izidor Hafner (April 2014)
Open content licensed under CC BY-NC-SA
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Details
To prove the construction is correct, it is necessary to show that the distance of to
is less than 1 and that the length of
is greater than 0.
References
[1] J. E. Littlewood, A Mathematician's Miscellany (Russian edition), Moscow: Nauka, 1973 pp. 141–143.
[2] V. Devide, 100 Elementary but Difficult Problems (in Croatian), Belgrade: ZIUSRS, 1965 pp. 87–89.
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