Lake 2
Three brothers were at a cottage on the shore of a circular lake. Every morning Andrej ran around the lake. Simultaneously with him, Braňo jumped into the water in front of the cottage and swam so that he was always midway between the running Andrej and the cottage. Dušan fished from a boat which he had anchored so that the swimming Braňo was equidistant from the boat at all times. How far was the boat from the cottage if the diameter of the lake was 1000 metres?
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