22th British Mathematical Olympiad 1986 Problems

22th British Mathematical Olympiad 1986 Problems - Further International Selection Test 1.  A rational point is a point both of whose coordinates are rationals. Let A, B, C, D be rational points such that AB and CD are not both equal and parallel. Show that there is just one point P such that the triangle PCD can be obtained from the triangle PAB by enlargement and

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