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RU-ALLRUSSIAN 1965 Problem 14

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A spy- plane circles point A at a distance 10km10\mathrm{km} with speed 1000km/h1000\mathrm{km / h} . A missile is fired towards the plane from A at the same speed and moves so that it is always on the line between A and the plane. How long does it take to hit?

Dataset text NuminaMath olympiads. Quoted with source.

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18\pi \text{ sec}

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