6th Vietnamese Mathematical Olympiad 1967 Problems
1. Draw the graph of the function y = | x3 - x2 - 2x | /3 - | x + 1 |. 2. A river flows at speed u. A boat has speed v relative to the water. If its velocity is at an angle α relative the direction of the river, what is its speed relative to the river bank? What α minimises the time taken to cross the river?
(2) ABCD is a rhombus and P a point inside. The circles through P with centers A, B, C, D meet the four sides AB, BC, CD, DA in eight points. Find a property of the resulting octagon. Use it to construct an equiangular octagon.
(3) Rotate the figure about the line AC to form a solid. State a similar result.
