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ASU 082 All Russian MO 1966 min speed of plane, angle changed

Source:

June 19, 2019
algebra

Problem Statement

The distance from AA to BB is dd kilometres. A plane flying with the constant speed in the constant direction along and over the line (AB)(AB) is being watched from those points. Observers have reported that the angle to the plane from the point AA has changed by α\alpha degrees and from BB — by β\beta degrees within one second. What can be the minimal speed of the plane?
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