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(367) 6

Part of 1993 Tournament Of Towns

Problems(1)

TOT 367 1993 Spring A J6 boat can move along a river

Source:

6/10/2024
The width of a long winding river is not greater than 11 km. This means by definition that from any point of each bank of the river one can reach the other bank swimming 11 km or less. Is it true that a boat can move along the river so that its distances from both banks are never greater than (a) 0.70.7 km? (b) 0.80.8 km?
(Grigory Kondakov, Moscow)
You may assume that the banks consist of segments and arcs of circles.
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