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060

Part of 1965 All Russian Mathematical Olympiad

Problems(1)

ASU 060 All Russian MO 1965 lighthouse enlights a ship

Source:

6/19/2019
There is a lighthouse on a small island. Its lamp enlights a segment of a sea to the distance aa. The light is turning uniformly, and the end of the segment moves with the speed vv. Prove that a ship, whose speed doesn't exceed v/8v/8 cannot arrive to the island without being enlightened.
algebra